EDIT: The below is completely wrong, ignore.
<del>The server-client model means you can run the server (MPD, Rockbox Zig, whatever) on your homelab, and stream music to multiple clients. So you don't have to copy all your music onto your phone, you can just run an MPD client like M.A.L.P. and it will stream from the files on your server. Then there's just one copy of your music collection, tags, etc.: no more keeping tags up-to-date between the copies on your home server, your laptop, your phone... (Do make sure your files are backed up, of course).<del>
If anyone is looking for opensource software that actually streams to multiple clients, check out Snapcast.
You got it 180 degrees wrong. MPD means many clients can control one playback server.
Thanks for the correction; edited my comment accordingly.
MPD doesn't really do streaming. If you install MPD on your server and then install an MPD client on your phone, the music will play on your server when you press play on your phone. You can re-encode the playback as an audio stream and stream that to your phone, but it's not really what MPD is built for.
Thanks for the correction; edited my comment to ensure nobody gets confused by my mistake. (I'm brand-new to using MPD, just installed it last week, so I had things backwards in my head).