Qt?

Only if you want to have fun writing your own bindings for the majority of OS APIs.

Qt for mobile devices requires the use of QML (not C++ widgets) and many APIs aren't wrapped, or even fit into the OS application lifecycle.

It is easier to use standard C++ and do your own bindings to Java and Objective-C, than QML (one version for each device) + Qt/C++ + wrappers into not support APIs.

Xamarin teams take the effort to create .NET bindings for all new iOS and Android APIs, on each OS release.

Not sure what you are referring to here. The benefit of Qt for me is that it wraps more APIs on more OS's than anything else I have come across. You can run your app on Qnx even Windows CE. It's incredible. You write your view in QML and logic in C++ with libraries that are so much saner than e.g. Boost. Then communicate between the two with signals and slots which integrate seamlessly with the dataflow property system. It couldn't be neater from my point of view and I have used a lot of gui frameworks.

From your answer I take you never tried to use Qt across iOS, Android and UWP.

Hint, the overall experience isn't like on the desktop.

I like Qt, especially the desktop part. I haven't used QML at all, but started using Flutter. Killer feature in Flutter is sub-second update times preserving the same state app was running as before. Is this doable with QML?

(Juce, a C++ ui framework, has also been a contender, and to a degree Lispworks, possibly others, but these are the ones I'm a bit familiar).