What’s the difference between a pistol squat and a single leg squat? In the pistol one, you go lower and have to bend your spine. Nothing else. When cycling, you never bend your knees as much as you have to do when pistol squatting with full depth, so what’s the point?
A pistol squat doesn’t resemble cycling efforts more than a single leg squat with a straight back and the resting leg beneath/behind you. Pistol simply requires ankle and spine mobility, while the greater depth increases the range of motion and difficulty of each repetition.
When squatting with a barbell, you must never bend your spine like in a pistol squat, so if you want to squat with full depth most people need lifting shoes with an elevated heel because of ankle constraints. If you don’t use lifting shoes, you either need to bend your spine in the bottom (“butt wink”) or stop before full depth is reached.
Low bar squats are different. Since the bar is lower on your back, torso more bent, hip constraints become an issue before ankle constraints, so these can be done without lifting shoes.
To me, this discussion seems to be a case of people not trying the movements themselves or they can’t picture the center of gravity in the movements. If center of gravity shifts back, you’re falling on your butt, hence the head, arms, knees over the toes - to stay in balance.
Look at the picture of Chad. He’s balanced, his spine is bent, his ankle is bent - center of gravity is in the middle.