I agree with the belt statement also. My typical workout for squat is as follows:
Bar x whatever - no gear
135 x whatever- no gear, pause to stretch at the bottom, hips are always very tight
225 x 5 or so- no gear, pause to stretch
315 x 2 or so- belt
singles the rest of the way to the working set, which depends on the day
405 - belt / wrist wraps
455 - belt, wrist wraps, light knee wraps
495 - belt, wrist wraps, tight knee wrap
545 - belt, wrist wraps, crank knee wrap
Anything above 545 I'll do the same, but I'll add water to my knees to get even tighter of a wrap. going above 545 is in the 90%+ range though.
By going this route, the 405 is one of the harder lifts because I'm still tight, and it's a pretty big jump in that range. 455 is much easier of a lift, and 495 is maybe even easier.
I feel this allows me to squat heavier, regardless of wraps or not. And, when you get to squatting 600 lbs +, it takes for god damn ever to get to your working set, so the less recovery between sets the better for me as I only have an hour to lift over my lunch (90 minutes but I have to shower and drive).
I feel, and this is just a personal preference, that training in what you compete in is paramount. So, train in wraps, not without wraps. Wraps get me out of the whole, and not using wraps may increase my getting out of the hold strength, but it won't help my core. If I can only squat 450 without wraps, and 600 with, then my core gains more from the with wraps, and that just happens to be my weaker point, the forward lean / sitting back into the wraps.
Also, you mentioned people dont' use wraps until a few weeks out of competition. I'm sure many people do this, but I also know that many people don't do this, Lillibridge for example (Eric, not Earnie, I think he goes sleeves until competition like you said). But, he's also doing 900+ for reps, so there's that, I think my knees would fall out of my skin even if I was that string without wraps.