That will totally lead to websites not supporting or even blocking Firefox.
A lot of websites that really should be testing for this don't work on Firefox.
Absolute worst case Firefox can focus on feature parity(as it already has a lot of), and lie on the UserAgent
For a while I think it was Papa Johns, or Dominos, some pizza chain site didn't work on Firefox. Worse than that though when I was in highschool I remember some school district stuff didn't work on Firefox