The many school traditions go back to middle age European monasteries part is true, the fidgeting part... poetic license.

And it is true that some task require quiet. Math is one of those tasks. But I as an adult have no need to fidget all that much.

And if I remember correctly, what you learn in the early grades doesn't need that much sensory isolation, I image things quiet down during exams.

So I think the degree of stillness can be slowly increased until you're expected to sit completely still in college.