If you agree to a school policy and them blatantly (or not so blatantly) ignore the policy you send a horrible message to your children. Probably a worse message than many of the “off limit” internet sites have to offer our kids.
The “internet” is not treif, although the vast majority of the informaiton avaialble via the internet is certainly contrary to torah hashkafa and includes many violations of halacha. Assuring “the internet” is like assuring chicken because an unscrupulous person sells treif as kosher. There IS a lot of kosher info available on the web, for personal and business use and with the proper “hechsherim” in place (filters, restricted sites, white lists – IE only selected sites available and no other url opens) “the internet” can be used and benefited from in a kosher way.