I suppose airlines would probably enjoy it if it reduced flight times a bit, but:
Aside from the most obvious reason (wind), I believe all ATC facilities operate in accordance with pre-established procedures and traffic "flows" which are developed with safety taking the top priority, and convenience coming in second.
For example at my airport, controllers use a "North flow" or "South flow" depending on the wind (conditions are rarely completely calm) and even though we have intersecting runways, I'm sure that larger airports with parallel runways operate on the same principles. The idea (as I understand it) is to keep everyone moving in the same general direction; this helps controllers organize & coordinate everyone much easier, especially when traffic picks up. Let's say that you are using opposing runway directions for arrivals and departures, and all of the sudden a storm front moves in and the wind starts gusting; if you are using opposing runway directions for arrivals and departures it might add quite a bit to your workload to re-arrange everyone to use the same runway directions.
Another safety concern would relate to missed approaches & go-arounds; by having arrivals approaching in the opposite direction of departures, you decrease the margin of safety if (for example) a pilot mistakenly turns the wrong direction on a go-around or missed approach (and into the path of an aircraft on climbout). The same could be true for a departure that encounters an emergency on takeoff/climbout. These dangers would only be magnified during operations in poor visibility/low ceilings.
There is also the issue of many airports which have only certain approaches on certain runways (ILS is a common example)... that would complicate things as well.
Finally, the whole idea of using opposing runways for arrivals & departures is pretty 'nonstandard.' As time has proven again and again, standardization (especially when it comes to procedures) is the way to go as far as aviation is concerned.