Typically when something is behind a login, it denotes a private space intended for a particular set of persons given explicit access. It's senseless to block people from using agents if the same people would otherwise have access, unless there is an abuse of that access, ie. action which is to the detriment of the space. And though some of that does happen, it obviously isn't the full story. I have a Perplexica instance running locally that I sometimes use (but often don't as Perplexity does a much better job). Should that also be blocked?
Hmm maybe a civil case could be potentially made here too, re disability. By blocking LLM use, sites are reducing the ability of select users to reasonably interact with the content. Just could become a thing in a few years if this nonsense continues.