As 727EMflyer has stated, flaps are for low speed maneuvers only and they are not used above a ball park speed figure of 230 kts.
That's the way they are designed.
As we are speaking of take-off performance, the crew has to chose between reducing the runway length necessary for a given weight and in this case,they will use high flaps settings, or if runway length is not the limiting factor, use the lowest setting to improve climb performance.
In order to climb, one has to consider two factors :
1-The engine thrust (the more thrust, the better)
2-The wing characteristics.The best angle of climb will be achieved at the best lift-to-drag ratio (aka Cl/Cd).
If one considers this ratio, a clean wing will always have a better one than with flaps extended as the high lift devices generate an absolute hell of drag rise when extended.
Taking Glom's initial question a bit further, probably all aerodynamicists and all manufacturers dream of a perfect "mission adaptative wing" which could change its aerodynamic characteristics, like thickness and curvature during each phase of flight, thus adapting to weight or maneuvering requirements as need arises. Some of this concept is already apparent on modern combat airplanes through the use of the leading edge flaps.