Taking whats been said into consideration, how about it removes secondary effects, like Sheer Force? That way attacks are stuck as damage-only? I don't think people would run recharge moves that often since most pokemon cant make good use of them.
For example, an ampharos wouldn't get much use from hyper beam, while sylveon would, but onl because of pixelate. I think the ability could have the potential to turn a shitty pokemon into a fairly viable one.
What pokemon could use this sort of ability in the first place? Pidgeotto comes ot mind, it IS the mach pokemon after all.