There is a different way to do 20 rep squats that I haven't seen mentioned here yet. That is the rest/pause squat. Basically, you take your 10RM squat weight and complete your 10 reps, rack the bar, take a bunch of lung-filling breaths to recover a little (not too much), then shoulder the weight again and do as many reps as you can. Repeat this process until you've completed all 20 reps. This allows you to use a higher percentage of your 1RM for the exercise.
I've even seen guys use 20 heavy singles before, that would be brutal for sure.
Has anybody tried these?
If I used my 10 rep max then I would already be rest-pausing reps 5-10, unless you mean a 10 rep max that's a straight set, which would take even less time and have the effect of increasing work density.
Another thing to note is that the squat is more of an anaerobic exercise nearer to maximum weights than it is with cardio squatting. I find the breathing to be less of an issue. I suppose with a 20 rep squat the body tries to find extra fuel once the ATP stores are depleted.
It's hard deciding whether to get more rest and use extra weight for more total reps or less total reps but using only small rests to increase the intensity. Either way it's probably good to get conditioned to both.