Stuff like the iOS 13 page sheet modals being broken is still an issue - but there’s a set of present/dismiss callbacks in the modal manager you can override in your code to fix it
Not sure if you meant page sheet controllers for iOS 15 (the ones that let you pin it half way up). There have been implementations of this, but they all suffered from a kind of crappy animation when you overstretched the page past its allowed limits. iOS would normally force a layout, then animate between the last layout and the new layout. But since RN’s layout is asynchronous, iOS couldn’t perform the animation and it looked sloppy
The measure function you mention isn’t co-ordinated to the layout, so you could read it while a layout is pending and get old data - but that doesn't really matter for most cases
May I ask, does the New Architecture and Fabric not solve this problem?
In contrast, 2D UI frameworks like Flutter, Silverlight, and Flash replicate the system UI. In my experience it is possible to create a replica that visually looks like a pixel-perfect match but it is very difficult to make the replica behave the same, like the rendering the subtle layer transitions you talked about, invisible boundaries around gestures, and showing the navigation history stack. It is an uphill task and using the native system UI is a tailwind for Expo.
As an example, some time ago, it was impossible to implement those iOS large headers that shrink to small once you start scrolling. Even though they were de facto standard in iOS for years already. Also the heavy layering of modals introduced in mostly in iOS 15 were basically impossible. Plus they heavily rely on subtle transitions like the 2nd layer scaling down, moving back and top edge peeking out at the top, so that the user gets a hint where they are in the hierarchy... Not sure if all this stuff works now, but generally Expo & RN were very slow to catch up with iOS and you had to rely a lot on dubious libraries, ending up with messy patchwork.
All these minor details are extremely palpable, even by standard users, and the experience just always feels a bit off.