I was in a frum school in GG in the 1990’s and we had sports for an hour a week, and we had to bring our sneakers. After being reminded the first couple fo weeks of every school year, anyone who forgot tgeir sneakers had to JOIN IN the sports lesson, running skipping and junping, climbing on the apparatus, etc, in their socks.
The school did it for years and years, so i imagine that there were not too many complaints. i think that it was a brilliant idea, it taught boys basic concepts, such responsibility, taking care for their belongings, consequences of actions. etc.
i would have noproblem sending my sons to a school that did it today.
BTW, in those days we all wore grey socks, so it more embarrasing.