Absolutely - there's already a bill in congress for this - the GUARD Act: https://thehill.com/policy/technology/5858006-senate-panel-a...
On the All in Pod, Chamath Palihapitiya has also been pushing to require ID checks to use AI models. Free thinking and free speech are under attack.
Having an AI think for you is not free thinking and having an AI speak for you is not free speech.
I mean, we all pay via CC so it's bit like they can't know who you are if they wanted to.