If you want to actively use multiple profiles, start the browser with -profilemanager and uncheck "use the selected profile without asking on startup"
Maybe I'm misunderstanding what's going on here, but when I performed the OP's "steps to reproduce" it restarted on the same non
-default profile, even though I have "use the selected profile without asking on startup" checked.
Okay, I just discovered something. If you have two browser windows open, one with the default profile, and the other with a non-default profile, when clicking Restart in the non-default profile, it will indeed restart with the default profile just like the OP states (then you'll have two browser windows opens, both with the default profile). If you have only one instance of the browser running with a non-default profile and click Restart, it restarts with the same non-default profile.