Most things are probably fine, though Windows updates might do something funky or just put it back from where you threw out that trash.

But Edge is a different story. Microsoft in their infinite wisdom decided to make Edge, their web browser, essential for Windows Explorer, their file manager and desktop among other things, to function properly.

So if you get rid of Edge, things can get kinda fucky. I haven't looked into if someone has made a workaround, I know that there are modified "debloated" Windows installs that do some heavy duty mucking about in there, but I don't know if anyone's figure out how to give Edge the ax without making your desktop freak out.