Unless there is a plan to allow attesters that are independent bodies then this is absolutely a threat to the open internet, or what's left of it.
The biggest dead canary for me is the lack of calling this out explicitly by Google or Apple. We're left to assume that Google is hand-wavingly saying "don't worry we can take care of that" when the private companies already monopolizing parts of the Internet are the absolute last people we want handling attestation.
There are two risks here (examples follow):
1. hostile requirements - "the agent won't feature adblockers", or "scraping without explicit website permission must be forbidden"
2. prohibitive requirements - "the agent implements protocols X, Y and Z and adheres to standards A, B and C" - all of these may be reasonable things, but en masse they may be too much work to carry by anyone but a reasonably big vendor
Additionally these criteria must be verifiable, so user can't basically modify the agent, because then the attestation is practically void.