> The rendering engine doesn't really matter

I disagree. For the purposes of this conversation, I feel like it's the only thing that matters. The web doesn't benefit at all from a WebKit-based browser by Mozilla capturing some of the iOS marketshare. Websites will still have to cater to WebKit. Not Gecko or something new

> Mozilla is not exactly known for their friendly and refined UIs

I actually strongly prefer the Firefox app's UI to safari

> For the purposes of this conversation, I feel like it's the only thing that matters. The web doesn't benefit at all from a WebKit-based browser by Mozilla capturing some of the iOS marketshare.

I believe it matters because it shows Mozilla's ability to market their product (Firefox). If they continuously fail to capture user base on any platform, then what powers Firefox is of little consequence.

As an experiment, I just installed Firefox on iOS just to see what's up and honestly 4 screens of things to confirm before I even get to the browsing part? As a tech person I understood each of them of course, but no sane person would put 4 screens in a row blocking users from using an app they normally already know how top use. So no, I don't believe Mozilla has the required UI/UX skills.

Mobile browsers aren't sufficiently differentiated enough for a significant amount of people to bother changing the default. Does anyone really think Samsung Browser would get close to 1.6% if it were a free and unbiased choice?

Apple sets the rules, gets special access (new releases, features, platform changes, countless other things), and relentlessly captures their users into the Apple ecosystem/moat. You seem to think swapping the rendering engine is a trivial task but you're asking them to practically create a new browser. And for all that effort, you're still competing with an opponent that's basically cheating. I'm not sure why Firefox/iOS even exists, frankly.

Firefox on iOS exists so desktop Firefox users can sync their bookmarks, tabs, passwords and history. I use Firefox on my iPad all the time.

It does, actually. For example, the reason why no other browser has the equivalent of Firefox containers is because they are the only ones with an architecture that allows for such isolation. Users of Vivaldi have been asking for containers for years now, and every time the dev team explains that they'd love to do it, but it can't be done without forking Blink and doing some massive surgery on it - at which point you again end up with your own thing, and have to play catch-up every time Google pushes yet another "standard" onto the web.