You need an interface on your phone for remote payment. Most of them have a workable mobile web site, but notifications for instance aren’t available in that case. Yes App Clips cover that case, but it doesn’t look to me that it got much traction.

> accessibility is worse on the web than on the iPhone (can't speak for Android). For printing and sharing, might be right, but it's broken on websites often enough, too.

I see this as the main point for having other browser engines. Mobile Safari is horrible to select text and on many basic features. I took these limitations for granted until I moved to android and the browsers work so much better (not flawless, but pretty close). Basically in this day and age, there’s no reason why a mobile browser should be weaker than its desktop counterpart.