There exist block puzzles in both games of this persuasion. However in those puzzles, there is one switch to three blocks, or obstructions to help guide the blocks. I see no way of actually completing this puzzle with the given constraints. Allow me to explain.

The yellow/gray block here cannot move ANYWHERE until the gray/yellow inhabits that middle position, or else you will never get another one there, or in any of the places around the center. It it simply cannot happen, due to the sliding nature of the blocks. No matter how you twist it, they will never stop there. This is also going off of the assumption that we can only move one at a time. If we could move multiple at once, it would break the puzzle and we may as well have Phenom and Bardock stopping the blocks wherever they need to be stopped.
Once that middle block is filled the unused centerblock can only go to one of two places, since it cannot be pulled.. (See pictures 2 and 3 from my "Solution" post.)
From there, it is stuck. It is no longer a useful block. It is simply in the way.
Even if you inch your way around, you still end up with a dilemma of "I need this block to be here so I can fill this last switch but there's no way to move it there" like this

EDIT: The issue with this puzzle is that as you move forward, you make it more and more impossible to progress.