React Native is already ported to desktops but you need to write N times for N platforms. In flutter, you can write just once after choosing a widget set, assuming you don't mind the same widgets everywhere.
Nothing stopping it, nope. I'm surprised there isn't something currently.
That said, it isn't so bad using different render functions for different platforms. The state management and event handling should be 100% consistent.
Besides, going all in on a single render engine limits you to creating special "holes" to utilize controls native to the platform. Im not sure if flutter supports this, but I doubt it.
There is - ironically, by the owners of Xamarin:
https://microsoft.github.io/reactxp/
Hadn't heard of it practically at all since the initial announcement. It seems it's a very small team: https://github.com/Microsoft/reactxp/pulse