I like the concept, really fun way of turning a platformer into a puzzler. If you build it out further, really take to heart the idea of a "catch" where the obvious answer is to do "X" but "Y" prevents you from doing that.
As the music composer for my team's game, I selfishly agree that a simple soundtrack would make a huge difference in the presentation. Think about what the "story" or the "lore" of the game is. Who is the player? Who is the character? What is the reason for the mechanic? That can give you a lot for a composer to work with in terms of tone of the game and musical themes.
Definitely hope you do build it out though because I agree with the commenters, this could make a great mobile game.