If it's concurrency, is it something that could be done in a library?
As for parallelism, I don't think many SPAs and PWAs really need to be able to make full use of multicore for acceptable performance, do they? If you're writing heavyweight number-crunching code, that belongs either server-side or in a native application.
If you try to port Red Dead Redemption 2 to JavaScript, you're going to have a bad time. That's not the fault of the web, it's just not an appropriate choice of platform.
Like I said in another comment in this thread, the downsides of the web as a platform wouldn't go away by improving its support for parallelism or for concurrency. Web-based UIs would still seem clunky and half-baked compared to native apps, and they'd still use far more computational resources than native apps.
I also do prefer native, yet as mentioned, web browsers or web widgets as GUI toolkits are a fact and aren't going away.
Specially if everyone keeps pushing packaged ChromeOS apps, aka Electron.