That's because what is restarting, if I understand correctly, is Mutter. And under X11, Mutter is effectively an X11 client. But, under Wayland, Mutter is the compositor... it of course does still do compositing under X11, but under Wayland the compositor is also the display server. So you can't restart it without disconnecting all of the clients... kind of.
Crash recovery and graceful restarts of the compositor are things that should be possible and are being worked on, and ideally this will allow for well-written Wayland compositors to tolerate a variety of issues that would've been hard to on X11, but for now, Wayland compositors mostly can't be restarted. This is also why GNOME doesn't want too much complex stuff going on directly in the compositor, and can explain some other architectural decisions about GNOME Wayland that are otherwise peculiar.
I suspect that it's the appindicator extension that I am using which causes the problem, but I've not proven this. I'm still salty that they removed appindicator support to begin with, though.
Crash recovery and graceful restarts of the compositor are things that should be possible and are being worked on, and ideally this will allow for well-written Wayland compositors to tolerate a variety of issues that would've been hard to on X11, but for now, Wayland compositors mostly can't be restarted. This is also why GNOME doesn't want too much complex stuff going on directly in the compositor, and can explain some other architectural decisions about GNOME Wayland that are otherwise peculiar.