Now imagine a world where PWA is substantially implemented across all major browsers. Given this scenario, let's pretend Mark Zuckerberg invented Facebook in that environment. There's the case for PWA - some apps are more engaging (for better or worse) with push notifications, home screen access, offline functionality, and optimistic UI updates.
Do I care if my favorite blogs have push notifications? No. Do I care if my favorite social networks and messaging apps have push notifications? Yes.