It would be very wasteful to deliver them directly. In this architecture every app has to manage connections and this is not good for battery powered device. It also allows to unload apps from the memory but still get the notifications.

Using apple servers is not that bad after all. If you care about privacy than you can use encryption. The message is delivered to the service worker that can decrypt them.

iOS now supports web push so no third party tools are required. But requires the site to be a PWA and to be installed.