Sure, but it shows global replies, it provides global search, it's not O(n^2), it's not easily DOSed, and it's highly amenable to spam filtering, which are the issues you raised.
It's true that this solution doesn't work for private posts and DMs, but the n in O(n^2) is much smaller there, so I don't think it's as much of an issue for personal data servers to communicate directly in those cases.
AT works by the use of global relays which see everything.
Sure, but it shows global replies, it provides global search, it's not O(n^2), it's not easily DOSed, and it's highly amenable to spam filtering, which are the issues you raised.
It's true that this solution doesn't work for private posts and DMs, but the n in O(n^2) is much smaller there, so I don't think it's as much of an issue for personal data servers to communicate directly in those cases.