The QT client is just the daemon with some GUI stuff on top, you can run a MN via the QT just fine, but then your CPU/RAM/HD etc. requirements are all double because you need all the extra stuff for the GUI client to work, so you're having to run/rent a beefier server... why bother? It's easier and cheaper to use the CLI daemon.

Nothing stopping you from running a MN at home using the QT client if that's what you want to do though.