Maybe we didn't evolve to be experts, because the returns from achieving that level of greatness were not worth the extra time.

(Agreeing with particular part and expanding.) The most significant benefits we can expect while playing are those few instances where our play throws us into a situation we can't quite manage without engaging full concentration with a small boost of 'deliberate' effort. Deliberate practice amounts to actively putting ourselves in the challenging situation over and over again for hours at a time.

If we are following the evolutionary reasoning we can consider deliberate practice to be 'gaming' the built in learning mechanism. This is similar to an RPG character scumming random monster encounters for experience or, more to the point, going to the gym.