It's due to safety issues. I can lift a lot more than I do at home but I avoid it because I'd like to be able to get the weight off me if I fail and I lift alone. Same for legs when I deadlift and squat. My lifts are about 50-60% of my 1RM.
5 sets of 21 get you to 100 reps of a light weight and that helps you aesthetically, you get a serious pump even though it's not best for strength. I just kind of came up with it.
My old home program used to be.
5 sets of 21 bench
5 sets of 10 pull-ups
5 sets of 20 bent over rows (50-75lbs)
5 sets of 10 hang cleans-to-shoulder presses (same weight)
I used to do it as a circuit, one set of each one before moving on to set 2.
Trying to get back there in terms of volume. you can see it's a ton of volume for the glamour muscles at a lighter weight but if failure happens a spotter isn't really needed. To your point, it doesn't compare to a real gym workout in the slightest, but it's a pretty complete upper body program.
Rest-Pause sets are great. After reading how they work I can do them for legs and presses at the least.