kollelman – As you point out, the child or parent who wants to see what they shouldn’t can go to the corner store, buy a prepaid smartphone, and look at whatever they want. School or no school, filter or no filter, smartphone or flip phone.
Filters work as a “first line” of defense, so that a momentary lapse doesn’t result in a breach, as well as unintended viewing. They are not meant for a teenager or other enticed to the Dark Side.
Finally, if schools can dictate lengths of skirts (well past tznius by any definition), Snoods vs. Sheitels vs. Hats, and Kollel vs. working, they can dictate whatever they want. Unfortunately, your assertion in the middle of your third paragraph is not completely correct.