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.
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.