I don't think it can necessarily work for any kind of application, but for some simpler ones I think it's completely fine.
This is kind of my point - I'm not saying you can't have applications that are usable across multiple UX paradigms, and I'm also not saying you can't write a UX library that automatically translates at least simple applications with little manual effort.
I'm just saying this requires active buy in from application developers into the ecosystem - you can't just run everything on all devices and have it magically work (with usability comparable to current state of the art in single device applications).
Like websites nowadays being usually designed for mobile and desktop devices
It's true, but on the other hand, it's much easier to adapt your desktop app to a smaller screen than to rewrite it completely for another OS.
Phosh (Phone Shell) already exists and works quite well. I'm writing this comment from desktop Firefox running in Phosh on Librem 5 smartphone.
See also: https://videos.puri.sm/pureos/l5-convergence-purism.mp4
Using the same hardware for both would be super useful, but the software stack from the desktop environment upwards should be entirely different (yes, including most of the applications!)
There are some fuzzy boundaries - e.g. imo Gnome 3 has proven that a single experience can feel good on both a tablet and a single screen laptop with a good track pad. But I think paradoxically you need to take different approaches on different use modes if you want to provide true unity.