Why would anyone want to do 20 reps of barbell squats? Because, high-rep barbell back squats...
I'm a big believer in people doing things they enjoy to improve general fitness. If you are a gym rat that hates traditional "cardio" options, then high-rep squats could be the answer for you. Is it sport-specific? Well, probably no, not really. Unless your sport is squatting a barbell for a lot of reps, then high-rep squats aren't what I'd call "sport-specific", but having legs and lungs that don't quit are a plus for most people and there are skaters, cyclists, and climbers that call high-rep squats "friend".
...develop mental toughness
A single high-rep session, let alone a string of them, isn't just unpleasant - it can be downright frightening! Managing the physical and mental stress of squatting a hundred kilograms or more for 20+ reps is a skill worth learning.
...develop work-capacity and focus
Maintaining proper form and grinding out another five reps when every cell of your body is telling you to re-rack the weight makes a single, double, or triple effort feel almost laughable - "Is that it?". Now, please understand, I'm not saying that high-reps are going to improve your limit-strength - almost certainly they will NOT unless your 1-2-3 rep maxes are low to begin with. But, after a steady diet of high-reps, low-rep sets and sessions (which may be lower volume as well) will be easier to focus on and recover from.
...are a staple of many, many weight-gaining strength programs
It's pretty tough to find people that couldn't gain muscle on a high-rep squat routine. The problem is that most people either don't continue the practice beyond a single session, or they continue far beyond the point of diminishing returns. For the life of me, I don't know why anyone would WANT to continue a high-rep squat program beyond 3-5 weeks.
While I wouldn't necessarily recommend it for everyone in the gym, reps of 20 and beyond has a place in just about any competent squatter's training. It goes without saying that, unless you really have a thing for pain and potential injury, a high degree of technical competence and a short preparatory period are mandatory prerequisites to barbell squatting for long sets.
Thoughts? Comments? Personal Experiences? Please share them here, or send me an email. Look forward to hearing from you.