Well, I think I figured out the obvious workaround: systemd --user edit mpris-proxy
Put the following lines in the editor:
[Service]
Restart=always
RestartSec=10s
After that the service restarted itself (after having segfaulted two days ago) as expected! Now, this causes the service to always restart, even in the case of OOM, but I think with its 0.1% memory usage it’s small enough to fly under the radar 