For what it's worth, a lot comes down to what features the server admin has activated. I've heard many complaints about XMPP but this is the first I've heard someone mention lack of features as a problem with it.
I really like XMPP, and the extensibility it has is brilliant, but at the same time leads to a crazy level of fragmentation for the instant messaging use case. You're basically guaranteed that you can chat to others and maintain a buddy list, but anything much beyond that is a toss up, depending on the server used, how it's configured, and what client each user has.
When a client logs in, it is true that a server doesn't have to send messages back, but that's the goal of XEP-0313.
http://stackoverflow.com/questions/25982426/persistent-xmpp-...
There are implementations for servers, e.g https://code.google.com/p/prosody-modules/wiki/mod_mam_muc, but I have yet to see a client reliably supporting this.
But the benefit of XMPP is that a new extension can be proposed that does this if enough people want such a feature. Personally I would argue that a better approach would be to make Public MUC logs accessible and searchable via a web interface and to have the client log chats going forward from when they join (with offline messaging from the server so you don't have to be online the whole time).