As I understand, progressive here means that it will work as an ordinary website even if the extra features like Service Workers aren't supported by the browser.

For me progressive should mean, that features (like adding to home screen, push notifications...) reveals progressively. Visitor should show some engagement, before PWA start to offering those features. Definitely not on first visit. It's very trendy nowadays, but extremely annoying to cancel all those feature request popups. "Do you want to receive push notifications?", "Please install our app for better experience", "Add app to homescreen" ... That's not web I like. And yes, I do realise it's far from original definition.

I think that it would be better to remove popups and only show an icon in the address bar so the user can click it and grant necessary permissions. My version of Chromium shows an icon when a site wants to install a service worker.