I'm no mobile developer, so I don't really know what I'm talking about. Please enlighten me if you can. Doesn't push notifications on iOS require using Apple Push Notification service? That was my last impression I got when I talked with someone about it.
Yes, you send a request to Apple's APIs and they will deliver a push notification. It's very simple really. Now there are a lot of wrappers around that (like courier.com) and instead of using Apple's API you know use the wrappers API. That also often requires some kind of 3rd party SDK to be integrated in your app.
These services are supposed to make things easier and have additional features like SMS notifications and so on, but, well not sure, never really used them myself.
Right, that was my initial point. You can't self-host notifications as they always go through either Apples or Androids servers, with neither company provide a way to self host that part.