Every time Twitter or Instagram bring up their custom share sheets I get super annoyed it’s not the default. PWA’s can probably get a lot of that, but a ton of web UX is arbitrary, unique, and more likely to feel janky in ways.
Even for well done web apps, like Notion, it stands out like a sore thumb when parts of the editor don’t work like normal Mac input controls.
I think PWA’s will have a lot of uses, but I don’t want them to take over either or Google get a browser monopoly. It’s bad enough how many devs don’t use anything but Chrome when testing. The web is what it is because it is not beholden to one company like the IE6 days
Also, Safari wouldn't vanish just because you'd be able to use a different browser engine. I strongly disagree with your "scary" (not scary) scenario: Only a small percentage of users is ever going to change defaults.
The growing number of device/browser combinations in use, legally-mandated web accessibility, as well as the expansion of expected web functionality to essentially require DOM and scripting abilities, including AJAX, made web standards of increasing importance during this era. Instead of advertising their proprietary extensions, browser developers began to market their software based on how closely it adhered to standards.
As soon as one browser dominates, one company gets to dominate how the web works. If you, as a user, want to be able to choose your own browser you should oppose one engine becoming dominant.