That is a really smart puzzle game! I think allowing the player to rotate things would make everything even more complicated and interesting. Another idea would be to allow the player to select their own blocks which they want to manipulate. But those are just suggestions, and maybe you prefer the game that way.
Though I didn't understand the last level and completed it by sticking the character into the box until the character came out at the top of the cube. Pretty sure that was a bug.