Only safari (webkit} shells. There's been rumors of apple preparing to open up that requirement for appstore approval, but hasn't happened yet as far as I know.
Honestly that, and not being able to side load, are the only things holding me from switching. Yes I could get a pixel and install graphene OS on it, but I don't have time for that anymore and I just want a simple solution that gets support out of the box, and allows me to run the apps I want.
I'm not going so far as to say I'd switch -- but I'd certainly get an iPhone and give it a try if it had sideloading/other app stores allowed (which in turn would allow other browser engines, since that's a store limitation). Would love to see an F-Droid equivalent for iOS start up.