Are 20 reps squats effective?
The question is "are 20 rep squats effective?"
I should start by saying that 20 rep squats hold a special place in the bodybuilding world. If I say 20 rep pull ups, I normally mean just that. However, 20 rep squat usually means that you would take your 10 rep max and get 20 reps not putting the bar down but resting as needed. Some variations exist - Charles Poliquin suggests taking 3 deep breaths in between reps. My favourite way, courtest of Ellington Darden, is one breath for the first 10 reps, then 2 breaths for the last 10.
Power/explosive strength - Better than no leg training at all, but basically, no.
Grinding strength - Not effective for 1 rep strength in of itself. However, the mental fortitude developed is excellent. Nothing teaches you how to dig deep and grind like rep 20.
Hypertrophy - Brutally effective. You're almost tricked into working harder than you usually would. The sheer length of the set jacks time under tension up. The limited breathing (in some versions) along with the constant muscle recruitment and blood vessel occlusion - even when you're "resting" - encourages lactate build-up. As the set is extended beyond normal limits, the larger fast-twitch fibres will be engaged much more fully than if you did 3x10 with the same weight. If you're using a decent weight the spinal-loading will be non-negligable and this stimulates the body to release growth hormone.
Basically, for hypertrophy, it ticks every box. This is the reason they feature heavily in the DoggCrap method, going under the name "widowmakers".
If you think they don't work, try this challenge. Pick a weight about 50% of your 3-rep max squat. Do a single set of breathing squats with the 10 1 breath, 10 2 breath style I described earlier. Each week, add 2.5–5kg. By the time you exceed your bodyweight, you should have seen some pretty significant hypertrophy, and maybe have a newfound respect for higher-rep training.