I think the Lack of Calf / Ankle flexibility issue is due to the coach not getting the athlete to Sit Back like you said. A lot of people just do straight down, the squatter knee drifting way past their toes until their calf’s/ankles stop the downward drift.
There should never be too much strain on the calf’s that somebody is inhibitated from doing a squat due to tight calf’s. I have yet to come across anybody who’s calf’s cannot at least make it to their toes.
The Box method is very good for beginners or those who just plainly got taught the wrong technique.
Another way, is to squat just an inch or two off a pole, keeping the face infront of the pole, and not letting the face drift away backwards or going to the side of the pole. You can initially hold onto the pole for support until you learn to go down