One (small) issue is that it assumes there *is* a client outside of the server. Most server apps have both a web UI and an API, and it’s even possible to build an ActivityPub server with no client API at all (microblog.pub was like that, IIRC). I think the ActivityPub C2S API was intended for servers that worked just like you’re describing, but IDK if anyone ever really implemented it properly.
On art sites - i.e. DeviantArt and the various furry sites that copied it in the 2010s (many of which are still very much active) - every user has a “favorites” page to which they can add anyone else’s posts. This also sends a notification to the artist. When I get a favorite or a comment, I always check that artist’s posts and their favorites page, to see what else they have favorited, and I can reliably find new people and posts that way. I don’t think this is really analogous to a boost, since it doesn’t show up in your feed, but it’s also not quite the same as “likes”, since it’s much more expected that people will go looking through it (people don’t really look at other people’s likes much, even though they are almost always public). Plus it’s almost guaranteed that it’ll be filled with art, as opposed to blog or microblog style text posts, so you’re not as subjected to the hot takes of random people you don’t know.