I have bad news for you. On iOS, Firefox and Chrome use the same WebKit as Safari (because Apple doesn't allow third party browser engines on its App store).
It's not as simple as that, you're basically asking browsers to target a completely different platform, just for the EU users, where iPhones are nowhere near as popular to begin with.
Google might at some point maintain two completely different Chromes targeting iOS, but I doubt anyone else will (including Firefox). Even with Chrome, I wouldn't bet on it. It's a very difficult technical problem with no clear, easily-marketable benefit to most people.
Apple knew what they were doing, they've "complied", but in a way where nobody would bother.
As far as I know a native Chromium port to iOS is well under way. Whether Google will release Chrome is a different question, but I think it's likely. I think Google would love to bring Blink Chrome on iOS everywhere and there is a decent amount of momentum with developers and regulators to pressure Apple into allowing third party browser engines even outside the EU, but that completely goes away, if no actual engine get's ported to iOS.
Blink Chrome on iOS probably gets a lot of enterprise web apps to drop WebKit support. That would probably that Chrome gets way more market share on iOS and with it lot's of telemetry for Google and also less money to Apple for default search engine placement.
It's not great for the web as a standardized platform, but it will probably happen anyways.
So Microsoft got dragged through anti-trust hell for just bundling IE with Windows and letting you install whatever browser you wanted after that, but Apple gets away with literally banning you from installing the browser you want on your own device, but that's ok? Make it make sense.
MS went through anti-trust investigation for more than just bundling IE, and at the time commanded a much larger market share¹ of desktop computing than Apple do of the mobile market now.
But while your comparison is flawed, I agree with the assertion² that Apple should not be locking user choice like this. The EU agree too, hence Apple's immature little hissy fit nearly breaking their (already "not quite there") offline-first app support for EU users when they were told so.
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[1] Avoiding the word "monopoly" to pre-counter the sort of "well actually" responses I got about dictionary definitions last time I said something like this.
[2] Unless I'm reading you backwards and you are saying MS should have been able to like Apple currently do!
You are not reading me backwards. And MSFT is worse today. I had to make changes at the BIOS level in a new Windows laptop to make it let me install Firefox without creating a Microsoft account. Was an ordeal just to get it to let me log in in the first place with a local only account.
They didn't totally get away with, the EU has set them to rights at least. It's just a shame they didn't use it as an opportunity to do the right thing globally at that point rather than sharding the market.
The Microsoft ruling in the US was that Microsoft was forcing third-party OEMs (Dell, HP etc) to ship Internet Explorer, not that they shipped it themselves.
As for the EU, they have already forced Apple to allow third-party browser engines under the DMA, as well as are forcing Apple to show a "browser ballot" like they made Microsoft do.
Microsoft’s anti-trust lawsuit with the DOJ was 23 years ago. There are people working at Microsoft and Apple who weren’t even alive when that happened.
The market shifted, and two decades passed. Most importantly the courts have been packed with jurists from the Federalist society, who are libertarian. As a result there are far more judges willing and able to throw out consumer protection cases such as what happened in the 90’s with Microsoft and IE.
They even have emulators now. Undoubtedly a change forced on them by the EU.