If you can't think of any companies that have built significant desktop apps recently, you're just not looking. I don't even get how this is an argument. "Well I haven't personally installed a native app recently, so obviously they're unimportant."

You know what's never going to go out of fashion? Performance. Especially since CPU speeds have stalled in the last decade. you will never get good performance if your design is: "embed an entire browser, and then use a small piece of it"