There are no other browsers on iOS. When you are using Chrome it is using UIWebView (in other words, it is forced to be a crippled Safari due to anti-competitive policy). Although recent Chrome will be using WKWebView which means at least it's same as Safari. The UI around the browser is not the browser.
> Few users cares for logging into some website from mobile Safari just to get a subpar experience over a native app (or a hybrid app),
Few users could tell any difference between native app and web app running in a browser that has modern appy capabilities, provided there is same quality of implementation. The only thing that can make the experience subpar is precisely the lack of capabilities.