Here's my pitch for a better ecosystem: we develop an intermediate standard for fundamental UI building blocks (divs/blocks/layers, images, video, etc.) + a layout engine, sort of like the DOM. Shells (browsers, native platforms like React Native but without the React requirement, etc.) would give JS renderers access to the lowest level painting calls available (ie. "repaint this node") along with programmatic access to the new standard UI API. Renders could then build on top of that API, implement the draw call optimizations themselves based on whatever makes sense for the rendering engine (for instance, React Fiber would be issuing draw calls differently than Vue's rendering engine.)
This would allow developers to get native performance out of a web-based rendering context. It would also be theoretically easy to build new renderers around the standard UI API. So you could swap out your backend between browser-native and a mobile/desktop library backed by OpenGL/WebGL, or another headless solution, etc.
Importantly, I think you need to limit the scope of this new UI standard (perhaps just to basic shapes, like how SVG is similarly limited), that way you leave UI implementations like dropdown boxes to ecosystem programmers (so you'd have a dropdown box for each React, Vue, etc. -- this sounds bad but people do this already.) Limiting the API scope also means making it easier for new renderers to enter the scene. Compare such a world to the current hellscape that is building your own HTML renderer. The API is so insane it's really only possible for big companies to take it on (Google, Microsoft, Apple, Mozilla.)
How this ties back into this post: you could create an _____ Native, which would really just implement everything you want from React Native, but without React. Then you can just plug Vue or React into the renderer and boom you're done.
Edit: Observant people will notice my ideal system resembles X11. Indeed, I think X11 is an interesting proposition in "shell" (browser, native) contexts, as shell applications are inherently window-managed and sandboxed. This allows for applications to reinvent the wheel without disrupting the fundamental UX of window management on the system OS.