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.
That said, the very vast majority of Wayland compositors, including Mutter, Weston and everything using wlroots, is implemented without separation between the display server, compositor, etc. so in practice this is still mostly true, it just needn't remain true into the future.
I do think, ironically, that the future of Wayland will involve making it more X-like - adding WM support, maybe stripping back the exceedingly overcomplicated protocol (my window manager is smaller than most Wayland example clients..)
And thanks to the extensibility of the Wayland protocol, you can layer any X functionality right back in...