Because, as I said, they have users using the app. They have said "we will not sell this app anymore", but they typically do not extend that to "we will no longer support existing customers for this product" (and even less so to "we will take this app away from those customers who downloaded/bought it")

By "even less so," you mean "never," right? Because they literally never have.

Disabling a feature within an app != shutting off push messaging. The first doesn't use Apple's infrastructure. There aren't a lot of apps that have been permanently removed from the store by Apple, and I can't remember if any of them used push messaging, so I can't be sure, but it seems reasonable to infer that if an app is permanently removed, its APNS profile might be automatically removed as well.

I meant "I don't think they ever did, but I am not sure, and don't want to see replies discussing this minor point".

As to disabling push messaging: I think this is a bit of a gray area. For some apps, push messages are minor features. for others, they can be an essential part of the app. Disabling them for such apps is equivalent to removing the app from the user's device.

I haven't seen the AppGratis App, so I don't know what push messages mean for that app.

They're pretty essential.