There is still a difference between "fetch this page for me and summarise" and "go find pages for me, and cross-reference". And what makes you think that all AI agents using Tabstack would be directly controlled in real time with a 1:1 correspondence between human and agent, and not in some automated way?

I'm afraid that Tabstack would be powerful enough to bypass some existing countermeasures against scrapers, and once allowed in its lightweight mode be used to scrape data it is not supposed to be allowed to. I'd bet that someone will at least try.

Then there is the issue of which actions and agent is allowed to do on behalf of a user. Many sites have in their Terms of Service that all actions must be by done directly by a human, or that all submitted content be human-generated and not from a bot. I'd suppose that an AI agent could find and interpret the ToS, but that is error-prone and not the proper level to do it at. Some kind of formal declaration of what is allowed is necessary: robots.txt is such a formal declaration, but very coarsely grained.

There have been several disparate proposals for formats and protocols that are "robots.txt but for AI". I've seen that at least one of them allow different rules for AI agents and machine learning. But these are too disparate, not widely known ... and completely ignored by scrapers anyway, so why bother.