You mean its actually possible to climb up flat, solid walls, a la Gang Beast style? I've tried but without success.
The game feels like it is designed without this in mind. Ledge climbing as it is already breaks almost every puzzle, as you can skip them if you know which ledges to use. But that's the thing; I had to figure out which ledges to use. I had to find the best route to go when I wanted to overcome an obstacle. Essentially, I solved another puzzle while skipping a puzzle. And that's great!
I don't want to be the man who makes the final decision, but I think the game would benefit greatly without "hand over hand climbing". Just my two cents.