Thanks for the comment!
Honestly you are the first one who thinks that wall jumping wasn't necessary. You must be pretty good and are experienced with platformers. Most of the people who played my game (me included) don't really have total control when it comes to high jump (holding down jump). We normally forget about that and just do a light tap. That's where the wall jump comes in: a generous secondary jump that can give the player one chance to fix their initial jump.
But there were a few places in my game that required the wall jump - now I'm really curious about how you beat it with only 2 wall jumps...
Live stream maybe? xD