A big part of education should involve preparing students to operate in future jobs and with the world. You absolutely need to know how to search the internet, discriminate between reputable and poor-quality sources, and arguably to use AI.
The purpose of education shouldn’t be to give an appreciation of Shakespeare for Shakespeare’s sake - it should be to speak and write the common language of the country, understand math, and prepare for their role in the real world. That role will involve the internet: only the Amish can really get away with someone else running their web presence.