I wish Newgrounds would also find a better solution than its current Windows-based Flash player to play its enormous Flash games collection (which currently still works in browser, of course)

It should be possible to make a Flash player that works for the most part using web technologies (e.g. WebAssembly). I remember Mozilla created Shumway (https://github.com/mozilla/shumway) but it looks like they have given up on it.

I believe that's exactly what Newgrounds is doing. See https://github.com/ruffle-rs/ruffle