With every release Android makes it harder to have a service running in the background. With the introduction of doze there is no alternative to using FCM. FCM has a privileged service where it is able to wake up the device from doze. A custom push service will never be able to do this.
There might be hacks, but I'd rather take Googles approach than to work around on each and every release.
Another difficulty was caused by the Doze mode, introduced in Android M. The Doze, which is turned on after a period of inactivity, among other things prevents background processes to access the network. As you can imagine, this prevents our app from receiving notifications.
We mitigate this problem by asking users to make an exemption from battery optimisations for our app. It worked fairly well.
This is why we were migrating to FCM from our own custom built MQTT solution that was invented back in 2012.