I've always hated it and thought it was a stupid untuitive mechanic that didn't map to anything in real life. It also looks equally stupid in multiplayer when you see player character models spasm their way up a ledge during a crouch jump. It's an old school mechanic that I am glad is going out of fashion due to better vault controls.

like a simulation of pulling your legs up in real life.

You don't pull your legs up in real life though, you use your hands to vault onto something. You can't just swap stances in mid air without holding onto anything. Even if you were talking about box jumps, like the kinds you normally do at a gym, it still isn't anything remotely like a crouch jump. Also anyone doing a box jump in an actual combat situation just looks goofy.

Any time a game explicitly has a tutorial for crouch jump, my immersion is completely broken. I am instantly reminded that it is a game.