I think you've put your finger on an interesting point, but it's not so easy. Since every tile in the 2x2x2x2 cube is effectively in a corner, it has only 4 valid neighbors. This is the same number of valid neighbors as the 4 interior tiles of the 4x4 game. The other tiles have 3 and 2 valid neighbors.

There's another thing. It can take more moves to put a tile next to another tile in the 2x2x2x2 game because of these degrees of freedom.

It's not clear to me how this shakes out with gameplay, and I've already wasted enough time on the 4x4 game that I'm scared to try the 4D game to find out!