It’s about convenience in most cases; an “app” to tap on, not a URL to remember and enter or a bookmark to save, name, file, and locate.
Just like apps in general, PWAs are mostly a mobile heavy modality. Bookmarks and the browser is largely still fine on laptop/desktop, but even there you see the app design language start prevailing with things like bookmarks and “recent sites” being presented like app icons.
It's not about power users. It's about regular users and the patterns they have learned.
The mobile ecosystem was built in a way to funnel all users into apps. That's the experience that is optimized for use, that's the experience users feel safe and secure. Barriers were put in place on what apps are even allowed to do (like not having alternative app stores, or a browser in iOs that is not just a webview of Safari). This created an enviroment where developers and companies are forced to develop to this ecosystem, and pay the Apple tax, since that's where the users are. And an alternative system is impossible to be created since Apple uses it's power at the hardware and operating system level to make alternatives impossible.
And someone will probably come and say that this is all users choice to be locked down in the walled garden. That the walled garden is keeping the users safe, so therefore it is only fair that Apple gets to capture 30% of all digital economical activity.
I swear it is so alien to me. Tapping on an app is equivalent to tapping on a link in my bookmarks.
Even if it's not a PWA, on both iPhone and Android you can create an "app icon" that will open a URL in a chromeless window. It's as simple as tapping "Add to home" from your browser.
So you get your "app" to tap on.