I was thinking the same, but as the pictures on the EXWM site suggest: could you not run a dedicated instance for the window manager? And do all your other Emacs tasks in embedded instances, so that the former is not so likely to crash?
But you can, of course, launch a graphical Emacs within EXWM. There you get a second Emacs thread.
One can also put X11 buffers in char-mode to pass through keybinds directly to that window. That way you don't have to do weird sequences to pass through emacs keybinds to another Emacs.