You've already mentioned some of the flaws of having a single button with a precise platformer, but you did a good job on capitalizing on some solid level design to test the limits of one-button controls.
I was torn on how much to rate you for design, because the individual levels show some really good combinations of different obstacles, but there are some obvious design flaws in just using a single button. Considering how well you designed the levels in spite of the forced restrictions, I feel that this game needs to be mentioned by GMTK, due to the lessons this game can teach about design. I'm giving full points for design, theme, and original use of the restrictions.
All that said, this was a truly terrible game. I'm glad I'll never have to play it again. You're an amazing level designer to get me to finish something with controls this bad.