Depends on how you do it, I guess. Squatting low weights or just body weight indeed doesn't involve stabilisers very much. But try squatting 2x your bodyweight on the bar and you find that it takes everything you've got to keep the body stable.
(Note: don't actually try to squat 2x your bodyweight unless you have some years of experience in squatting and know what you are doing)
That's... kind of the point. Building your stabilisers with heavy weights only can be risky (especially if ego comes into play). Implementing accessory exercises to build stability / balance / flexibility alongside your heavy lifts is a great insurance policy for beginners. (whether Yoga is the greatest source of those is another topic, especially when considering the many different forms of Yoga many of which have a not very evidence based origin)
(Note: don't actually try to squat 2x your bodyweight unless you have some years of experience in squatting and know what you are doing)