You absolutely need push on iOS and modern Android. S60 and Android before doze didn't because you could just have a connection in the background; afaik, BlackBerry didn't restrict background data either. But it's not like there was a lot of good mobile XMPP clients that died out when push became mandatory.

If there was, it wouldn't take much to make an XMPP extension or three for the client to provide a push url to the server. Client devs would (probably) need to standup a push proxy, so xmpp server pushes to client server pushes to client, because I don't think many platforms give out push urls that can be securely passed on to 3rd parties. There's some expense there, but not a whole lot, IMHO.