You should compare it imho to ssh. If you break your connection, your session is gone. So if you only want certain parts of your session survive, which ones should? Because maybe your container depends on avahi on the host, or cups, or...?

Just a random thought, but if you can create a user on the host that just has the most minimal set of systemd services enabled your container needs, you could apply it to that user.

But still, on a server that wouldn't make much sense imho, as the default user is usually the service user having a minimal set of services enabled. On a desktop, your default user is logged in anyways. So I think this isn't a real problem tbh.