I think this is very silly. I dislike the whole AI hype as much as any other. But by that standard you could also ask "Should Photoshop also pay taxes?" or "Should printers also pay taxes?"
If we are oh so productive that people can make oh so much money then A) finally do collect taxes from wealthy people/companies/families and B) use those taxes to do obvious things that benefit everyone including the wealthy, like good infrastructure, healthcare, stuff that creates a stable society and seduction to face all the big problems that exist.
There are huge problems in every country and since the claim of AI is gonna create so much more productivity and wealth we should make use of the freed resources to finally tackle them instead of pushing everyone into dumb bullshit jobs.
We live in a world where rich people (and it doesn't really matter which country) use their companies to essentially live off taxes. "Oh that computer/car/jet/travel/video game/TV/house/...? I need for work. Look I have to fly to customers and oh I also have that social media thing for advertisement". Oh and then they claim they'll just leave the country if they have to pay taxes which would be oh so bad for the country they don't contribute much to.
And then the employees are essentially asked to pay the taxes to compensate. For them tax reduction means that they have to pay for things like infrastructure that largely benefits corporations themselves. But hey it looks great on the paycheck when the money you have to pay anyways isn't subtracted.