That’s not the kind of crouch-jump that’s being discussed here. In source games you can crouch while you’re in the air and it allows you to reach slightly higher ledges. It’s got nothing to do with the long jump upgrade.
I always saw it as a quirk of the way the game is programmed (they didn’t bother disabling crouching while mid-air) that they just ended up somewhat legitimising by teaching it in the tutorial. AFAIK you only have to use this once or twice in the entire game, and don’t recall it ever being useful when not forced (maybe except for climbing where you shouldn’t to sequence break).
It’s not part of the core gameplay. You learn in in the tutorial, forget about it, get stuck in the middle of the game, remember this is a thing, use it once and then forget about it again.
At least that’s how I remember it. It’s been a while since I played HL1.