In the interests of compromise between Field Length and 1st/2nd Segment Obstacle clearance climb, V2 is often minimised, primarily a Field length consideration. V2 min is most often somewhat below the best gradient speed available, but necessary due to field length constraints. As John_Tullamarine has indicated, allowing the speed to climb above V2 will consume climb gradient, thus providing less than satisfactory obstacle clearance.
Most (good) AFMs advise a maximum speed to be flown in the event of engine failure above V2 (V2+10, V2+15 etc). This recognises that an improved gradient is possible at these speeds, PROVIDED THAT the engine failure occurs after V2 has been passed. Accelerating to these improved gradient speeds WILL reduce your gradient during the acceleration, perhaps disastrously.
This gives you 3 options -
(1) If failure occurs between Vef and V2, follow the AFM pitch attitude recommendations for acceleration to V2 and then hold V2. This is allowed for in the airborne portion of the Takeoff between Vef and reaching V2 at the Screen Height,
(2) If failure occurs between V2 and the AFM recommended additive (e.g. V2+7 where the AFM has stated 'Not above V2+10'), fly the EXISTING speed without deceleration or acceleration,
(3) If failure occurs above the AFM recommended V2+X, reduce to V2+X, and maintain that speed.
That's how they're certified.
rhovsquared, 737s, 757s, 777s, A320s, etc are NOT over-powered. Sure, on many occasions, there's performance to spare, and we use Flex / Reduced Thrust, but I've done numerous Takeoffs where we NEEDED to use every pound of thrust available.