Then roll your own implementation that can support lobbies from different services, like many games already do just fine. Don't launch a separate launcher within a launcher, it's stupid.
Which is extremely ironic because Fall Guys has the epic overlay that includes perfectly fine and working friends connection with any platform, including switch, PlayStation, epic launcher, and steam friends list. We play weekly. Why doesn’t every EGS game do this?
Edit: That is to say, a game launched via steam and on consoles works just fine without EGL.