At least on iOS, Apple controls the singular web browser implementation. If they wanted to, they definitely could do a thing about any site. The same arguments for policing their App Store would apply to the open internet too, it's scary and dangerous!
Sure they can. Mobile users have no path of recourse if Apple updates WebKit to break or blacklist the site. There is no working alternative on iPhone or iPad.
Maybe the people advocating for browser diversity on iOS were onto something...
Yes, no recourse. But there are still legal consequences. If Apple blocks certain web content they have a harder time arguing that they are not responsible for blocking other we content: copyrighted material, etc.