Web apps provide stronger sandboxing, and protect the user more. There's a reason that Twitter and Reddit nag you about "installing their app" whenever you visit them in a mobile browser.

> Every website without fail that ever wanted me to allow push notifications did it just so they could spam me.

I think this is mostly due to iOS/Safari not supporting notifications. The more serious actors who want to provide actual value to the users have been strong armed by Apple to create a native mobile app. Conversely, if the only browser allowed on iOS actually supported push notifications, you would see more legitimate prompts for using the tech.