That's not really what I mean. The person I was replying to was saying that I can't get push notifications without Google's centralized stuff. ntfy/UnifiedPush appears to do just that, so I'm wondering what is missing here.
From what you're saying, it doesn't sound like the OS-based polling would be more power efficient, as someone in this chain suggested, just more reliable. Though, I think you can just turn off battery optimization for the ntfy app, in which case I'd expect them to be on par.
If that's right, it seems like ntfy with battery optimization turned off is effectively a "real" push notification system.