Chrome is available (and dominant) on desktop yet Firefox and a dozen other alternatives are doing just fine. There's no reason why it shouldn't be the same on iOS.
I wouldn't call that "just fine".
If not for Safari (18.84% market share) Google could just dictate what happens on the Internet, because Chrome-based browsers would be the de facto standard.
The only reason sites still bother to support non-Chrome browsers is the fact that people on iOS monetise REALLY well compared to other segments.
Sites work well in practically every browser because we're not living in 2005 anymore. Some missing APIs are broken, but how often do you really need WebSerial on your phone.
And therein lies the motivation to "open up" Apple's ecosystem, people just can't stand looking at all those dollar signs without being able to get their hands on them any way possible.
"So Apple just gets exclusive access to their users' money?!?" Well, they are the ones that built and maintain the ecosystem. Everyone else just wants to get in there and extract wealth like slash-and-burn rainforest developers or strip-miners.
Thus they go privacy first in things just because they can. Like randomising IDs used to identify players across apps and services. You should've seen the tears marketing shed when that change happened.
But the competition (Google) is by all measurements an ad company that does software and hardware on the side, they cannot go the privacy route. Ads require tracking and tracking implies privacy issues.
Firefox really isn't doing just fine, though Google might decide to keep them alive through browser payments just to not look like a monopoly.