Google already does this to a larger extent:

https://blog.pwabuilder.com/posts/publish-your-pwa-to-the-io...

It is Apple that has had issues with PWA support.

> While WebKit is making progress on PWA support, at the time of this writing, PWAs remain a second-class citizen on iOS. The iOS App Store’s support for PWAs is non-existent, requiring a web view-based solution like PWABuilder’s.

> Additionally, because iOS doesn’t allow 3rd party browser engines, your PWA is limited to WebKit’s PWA capabilities, which are currently lagging behind other browser engines.