Don't even need to go that far. Provide a locked-down computer and have students write essays in a dedicated space. I have personally done that and it was a reasonably good experience.
What would be the impact on democratic systems if voters always turn to an LLM for answers because schools didn't require them to think on their own?
Further, there are likely situations where the participants avail of AI to different extents based on how they feel about the situation (cf. different degrees of doping in athletics), and students will sometimes be limited by their means in use of AI tools.
People said the same shit about calculators in math class. Yes, you may have a calculator that can do calculus available 99% of your working life, but if you never learn even the basics of anything then you are fundamentally just a monkey with a typewriter.