(as an aside I really like Swift too and have been enjoying noodling around with it as a server language. Probably rarely a wise choice given that it isn’t their focus but there is some attention given: https://swift.org/server/)
I'm at the point now where native apps are still back in heavy consideration, as it's far more straight forward to cascade launch your products on different platforms than it is to half-ass everywhere.
Generally (IMHO) there are no good cross-platform stories, mobile or otherwise with the notable exception of some game engines. The closest you can get is choosing the web browser as your platform and writing a web app (Electron).
If you want to make the best app you can, use the native toolkit directly or via a framework for your UI.
There are browsers already installed, and MSHTML apps and XUL predate it for a decade.
I think you'd be surprised! There are some big names using it at scale[1].
Any equivalent of the above has to be hacked together using JS, which ties up the main thread and can never fully match the host OS.
At this point, the most straightforward technical road to cross platform UI seems to be building high level UI toolkit that runs on browser runtime (ONE specific browser run time), and "platforms" slowly integrating this runtime as their native and only behavior. Note that I say "most straightforward", not "easy".
Personally, I don't see any viable *business* road for this, but happy to read some fan fiction on that.