That's not entirely true!
If you had a straight-wing for supersonic use, or possibly if the shockwave swept back beyond the sweep-angle of the wing you'd use a symmetrical foil.
The reason is that the some of the principles behind a regular airfoil -- the curved portion of the top section of the foil producing a low-pressure zone on the top seems to go largely in reverse at supersonic speeds. Convex curvature increases pressure and slows the airflow down which reduces lift. AoA will have to be increased to negate this, and more to produce positive lift.
While inverse-camber would be better for supersonic flight as pressure would be increased on the bottom, it often isn't exactly the best choice as the design would produce negative lift at subsonic speed requiring higher AoA's to get positive lift while subsonic. Since supersonic foils are kind of thin, this could make takeoff speeds very high, and critical AoA's quite low. So instead symmetrical are typically used since it's the next best thing. Sure at 0-degrees AoA it produces no lift, but once you get the AoA up you start producing lift. It produces better performance at supersonic speed than a standard subsonic airfoil, without substantial losses at subsonic speed (although there are some losses). I should note that even with this said, you will still require a higher AoA at supersonic speed as the L/D ratio falls off due to the thicker boundary layer, increased turbulence, and a lower pressure differential (the low-pressure zone up top isn't as low as at subsonic speed), but it would be substantially better than a subsonic airfoil.
These particular airfoils only have some limited applications. Straight wings experience a massive shift in the center of pressure (on a straight wing once the upwash up front goes away, the center of pressure shifts back to the 50% mark). This produces a strong nose-down tendency in supersonic flight requiring considerable longitudinal trim deflections which produce excessive amounts of drag if you're looking for endurance. Not to mention, the thickest point on the wing is often half way down the wing (due to the center of pressure being at 50% instead of 25% at subsonic flight) which does degrade low-speed performance (Still better than an inverse camber supersonic-foil). The airfoil-thinness can pose a problem as fuel might not be able to be carried in the design (the F-104 could not carry any fuel in it's wing and needed the fuselage to do the whole job). The serious advantage they do have is that they have very low drag when flow over them is fully supersonic compared to other airfoil types. They call this supersonic-drag. In fact even if shockwaves produced on the other parts of the plane sweep beyond the wing's leading edge, it's not that big a deal. Tapered, or trapezoidal wings (low-sweep) a'la the F-104 type will feature a shockwave that will form on the root and sweep back... even if they sweep back well beyond the wing's leading edge, it's not a significant problem. In fact, the F-104 aircraft's geometry (if airframe and temperature restrictions weren't an issue -- and they are) could easily allow for speeds in excess of Mach 3 maybe 4 (I've been told it's shape could allow for twice the speed if engine temps and structual limitations didn't matter)
There are other types of airfoils though used for supersonic flight though and a large number of them do not have fully-supersonic flow over them.
One example is a swept-wing. In addition to sacrificing span for a lower thickness/chord ratio (behaves better at high-subsonic and transonic speeds too), at Mach 1, the shockwave only forms off the wing-root, leaving the rest of the wing behind it, and as long as the shockwave is equal or less (or at least in *front* of) than the sweep-angle of the wing, some of the flow field will behave subsonically, at least the parts at angles to the wave (if you pointed an object dead ahead, you'll still get a shockwave). This subsonic effect enables one to design most of the wing (except maybe the root) with blunt leading-edges and such like you would on a subsonic plane, still achieve low pressure suction zones across the front, and retain some low-speed handling inherant in blunt-leading-edges. The subsonic effect only covers so much of the wing, the leading edges and a bit aft of that, but eventually it will go fully supersonic. Highly swept-wings generally have a lower shift in the center of pressure, and their stall onset is usually more gradual than a straight wing which is much more abrupt. They have some negative side-effects though including noticeable span-wise flow at subsonic speeds. The airflow despite the wingsweep at subsonic speed goes pretty much front to back over the wing (technically the inward spiraling vortices which are at the tips do cause the flow to slide inward a bit, but not factoring that...), on swept wings there's a tendency for the flow to slide sideways across the wing in such a way that could actually seriously reduce aerodynamic performance and even produce a stall. Stall fences, slats, and proper aerodynamic-contouring of the wing can deal with this problem. Another problem is flexibility. Swept-wings flex a lot which pose a number of problems, including aileron reversal in which the aileron deflections cause the wing's leading edges to twist in opposition nullifying and even reversing direction of roll. For supersonic flight there may even be a flutter-risk in some cases, although I'm not sure how big a problem that is. Swept wings designed for supersonic flight do often fly at higher indicated airspeeds as well which puts more stress on the wing during banks and turns, so they are often stiffened up -- this can result in a weight penalty. Tip-stall is the next problem, on a typical straight wing, it stalls at the root. Stalling occurs at the back of the wing where the flow has lost a lot of it's energy after flowing over the whole wing, so in this case it stalls at the inboard rear of the wing. This disrupts the downwash which is a downward flow off the back of the wing which increases the downward load on the tail (tails produce a negative lift since the center of pressure is behind the center of gravity which is necessary to produce stability), the reduction in downwash causes the tail to become less effective causing the wing's natural tendency to pitch down to take-over... once the wing's AoA lowers and recovers from the stall, the downwash is restored... On swept wings the tips tend to stall first, which along the span is much further aft... when it stalls, the inboard part of the wing which is further forward keeps lifting and the plane pitches up even further, AoA goes up with it and it makes stall recovery much more difficult than a root-stall. The solution involves twisting the wing such so that the inboard leading edge is at a higher angle of incidence than the outboard trailing-edge. Another problem that swept-wings have is known as dutch-roll, a type of lateral instability, believe it or not, not named after some kind of pastry, but actually the way that Dutch sailors used to stumble and roll all over the place while drunk on leave. Turbulence can cause yawing, which causes more airflow to go over one wing than the other, with swept wing, the effects of sideslip (which is like AoA on the sideways axis) cause one wing to dramatically produce more lift than the other -- the result is substantially increased roll rate over a straight-wing. Eventually the tail slows the yawing down and the plane starts yawing the other way, then causing another roll-rate in the new direction. It gets worse every cycle too. The greater the wing-sweep, typically the nastier the dutch roll... It's very difficult to correct because the amount of yaw input to cancel out the motion is often very little at high-speeds, and the pilot puts too much in aggravating the problem. There are a number of solutions which include increasing the tail area which would stop the yawing in its tracks typically, and the addition of a yaw-damper, a device which works through the autopilot and makes small movements to the rudder by detecting sideslip, cancelling out the motion before it is able to get too severe.
Another example is a delta-wing. The delta wing provides a number of aerodynamic advantages for a high-speed aircraft. It is naturally a rigid structure which does not require extensive structural beefening. It has a lot of external area which produces a lighter wing-loading than a swept wing could, and greater internal-area which allows for lots of fuel to be carried if needed. It's high leading-edge sweep angle causes a vortex to form at the root and flow spanwise ultimately merging with the wing-tip vortex, while the wing-tip vortex plays a role with downwash, it degrades lift and increases drag like any other... however the leading-edge vortex helps energize the flow over the leading edge causing the wing's critical AoA to be much higher than one would expect from that particular airfoil cross-section, even when stall occurs, the flow is still stable over the control surfaces mounted on the aft of the wing allowing easy recovery -- in stall, descent rate increases substatially though, however pushing the nose over will fix that problem. To my knowledge the same effect can occur with some highly swept (~60-degrees) wings too. Like highly-swept wings, the stall onset is more gradual than a straight wing, which occurs more abruptly. The delta-wing's leading-edge except the root rides behind the shockwave and as a result has a subsonic-flowfield over the leading-edges and over significant parts of the wing. This allows blunt leading edges as on the swept-wing and even a type of camber called conical-camber in which the leading edge kind of curves downward-- nonexistant at the root, and getting progressively more noticeable in terms of chordwise coverage and to an extent curvature as you get further and further down the span, with the curved wing often blended with a downward curved wing-tip which helps overall in the process, may even reduce vortex-drag. This conical-camber like blunt leading-edges will increase suction on the leading edge, increase the L/D ratio at supersonic speed and drastically improve low-speed handling. The problems with the delta-wing is while delta-wings may (due to large wing-area and vortex-lift) perform nicely at low-speeds, still take off and land at very high angles of attack which produces undesirable amount of drag. This reduces initial acceleration and climb-rate until the angle lowers a bit. Also, during approach it's very easy to end up losing too much speed with the AoA getting too high requiring large amounts of thrust to jack the speed up to get the AoA to a reasonable level for approach. Also, the difference in takeoff and landing speeds are further apart than you would see with most wings as well. Additionally since a delta is traditionally a tail-less design, the trailing edge of the wing needs to be deflected up which is contrary to what you'd ideally want on a wing, the problem is generally overcome once supersonic as the drag produced by having a tail would actually be more so than having elevons; at subsonic speed and transonic speed a tail produces an advantage. Delta wings because of their larger areas experience a greater shift in the center of pressure than highly swept wings. If the airplane is small like a fighter, the thrust to weight ratio should be able to overcome the trim-drag, larger designs would probably shift the fuel into rearward trim-tanks to put the CG and the Center of Pressure near eachother to provide low enough trim-drag. One of the biggest problems with Delta-wings, and it's not a huge one unless you plan to fly REALLY REALLY FAST, is that once the shockwave sweeps behind the wing drag increases to the point that a straight wing would be better.
Now there are other wing-designs that exists, but I'm rather tired right now and feel frankly like getting a good nap.