Not true, for example Opera Mini[1], perhaps others. I wouldn't jump to conclusions that fast.
No one is jumping to conclusions here. This is the specific result Apple wants and is by design of their policies. It's well known and there's no debate over it. You can have your own browser on iOS, but it can't interpret JavaScript (no interpreted code on iOS), meaning it's completely useless on the modern internet. It's the perfect way to enforce a one-browser-to-rule-them-all rule, locking out all competitors, while couching it in a 'security' guideline.
1) You can't ship your own browser engine 2) If you use the built in engine, you don't get JIT on (but Mobile Safari does)
1. Not being able to use JIT is just the anti-competitive part that Apple does to people who ship UIs/skins over Mobile Safari.
2. The more insidious bit is that you can't run interpreted code in your own app AT ALL, which prevents Google, Mozilla, Opera, etc from being able to ship their own full browser engine because it wouldn't be able to implement JavaScript AT ALL, making it completely useless on the modern internet.
So, you're left with Chrome on iOS which is just a fancy skin/UI over Mobile Safari (sans JIT so it's forced to be slower so Safari looks better by comparison). Compare that to Chrome for Android which is the full Blink-based browser stack tweaked to be as fast and smooth as possible. Or Firefox on Android which is the full Gecko engine with a custom Android native UI running over the top. You can't have the Gecko or Blink engines at all on iOS because Apple says so.
I'm sure it can be done, but that's the biggest reason it hasn't been done.
The only thing that's a dealbreaker for me is that Apple prevents all other real browsers from shipping for iOS. One browser only is a dealbreaker for me on any OS.
Yes, that's what they said for Opera 16, too, and 15. Last version of Opera to be released for Linux was the (pre-blink) 12.
I'm sure they will get around to it eventually, but I've personally given up waiting and switched to Firefox (mourning the loss of my beloved spatial navigation, which was why I'd stayed with Opera until now). (Being able to access all my bookmarks from Firefox for Android is a nice side-effect, AFAIK Opera still haven't gotten around to implementing Opera Link for Android version).
(On a more practical note, for why I switched to FF - the latest Presto may not be much more than a year old, but you'd be surprised how fast the web changes when you're using an unmaintained rendering engine. New website functionality often doesn't work - html5 file uploading on most sites is broken, can't get the new google maps, g+ and fb are slow, etc. Web devs don't test on presto now that opera for windows/mac doesn't use it, and opera have stopped packaging website shims).
(Note also that there had been large delays in Presto reaching Desktop before — most notably with Opera 10 (2.2.115) and 10.10 (identical but with Unite enabled), Mobile shipped a beta of Mobile 10 with Presto 2.3.something before 10.10's release, and a second beta with 2.4.15 shortly after. Note from late 2.3 Presto releases, the final digit is the most significant one.)