They're useful on desktop, for having things like Gmail open in the background, but they're not hugely useful on mobile. Usually if you want notifications you would already have the app installed.
The whole point is that if Apple would allow this, you wouldn't have to install the app. You could just use the website.
Forums are an example where the website is perfectly fine without an app, but I'd really like to be able to choose whether or not I get push notifications from them on my phone.
Forums are an example where the website is perfectly fine without an app, but I'd really like to be able to choose whether or not I get push notifications from them on my phone.