Yeah, that’s a fair use-case.
My assumption is that most people running a server will be running it headless. In this scenario, the easiest way to administer Syncthing is by exposing its web UI to other machines (properly password-protected), rather than RDPing in and using some tray utility. Therefore SyncTrayzor is pretty useless here.
For running Syncthing as a service, see http://docs.syncthing.net/users/autostart.html#run-independent-of-user-login and Syncthing Windows Installer. Pay attention to the warnings about running the service as an unprivileged user!