What are you talking about? I'm using FF without any trouble at all on both desktop and mobile for each and everything, and so do many others, for its support of uBlock origin if nothing else. Also, the iOS devices out there have only Safari-Webkit.
There are some hipster web-sites built by amateurish developers who manage somehow to make them work correctly in Chrome only. I've faced those too and after reporting the bugs (like horizontal scrolling of menus) the reply is usually something along the lines of "most of our users prefer Chrome, so we won't fix it".