Yes cube is too important, but i would not put its importance higher than that of checker play! Ask a simple question: Can someone that doesn't know to play a good checker play, have any possibilities to win anything good, even if he knows well when to double and when not?
The question of who has the advantage, someone with better cube play but inferior checker play against someone, is simply not well defined....
Anyway a general idea is: Checker play + Cube play are impartible! No one can go to the success room if he is good only to one of these....Both are needed.....