This seems like a very constricting protocol, though: the one-to-one correspondence between a user and a server means I need to individually post my activity to the "inbox" of everyone who wants to read it (or they poll my "outbox" - I'm not sure). Not a recipe for an efficient system. It's called ActivityPub, so this was clearly a design decision to meet the goal of being decentralized.
But I probably wouldn't implement this standard in a project unless I modified it a bit so that many clients could share a server.