That's correct. Even on the 3x3x3, where it may appear that some positions should be 2-gen friendly (solvable with only <R, U> moves), they are not. (Fun fact: For the <F, F', F2, B, B', B2, L, L', L2, R, R', R2> 3x3x3 move set, you are able to do a U or U' move, but a 4 edges must be...