I only watched level 1, but it made me wonder... so I tried TASing it myself.
This seems to be 144 frames faster for level 1.
Edit: I watched it completely now, and maybe because I already knew the game, it was entertaining to me. I don't know what other will think who aren't familiar with the game though...
I don't think however that the quality is as good as it should be. Besides that improvement at level 1, I also spotted improvements for instance for level 6 and level 16.
At level 6, you can pick up the fruit at the bottom right by jumping straight up, instead of jumping over the pit and back... when I completed the level, I also noticed that the spring jump at the end and the climbing wasn't optimized, so frames could be saved here also.
At level 16, you only make a low jump at the spring at the bottom right... a high jump would have been a lot better and saves half a second easy.
So I would vote yes to a TAS of this game (without skipping levels like the other movie obviously)... but since it can clearly be improved (I just tested some things I noticed... didn't do any real research or anything) I won't vote at this moment.
Edit2: Ah, I forgot to mention. There were some levels were I really enjoyed your solution, such as level 17, 20, 32 and 44. Most of these involved going from one side of the screen to the other.