I have been working and running ntfy [1] on my phone for a year now (ntfy is a UnifiedPush distributor), and it is true that Android does kill the app every now and then. But it is instantly restarted. Usually ntfy delivers notifications much much much faster than Google's FCM, especially in doze mode. FCM seems to try and conserve battery much more.
Sadly, I had phones where I couldn't keep anything running. Not sure what the manufacturer did there. Even the normal notifications didn't arrive at times. (E.g. Signal)
Disclaimer: I am the maintainer of ntfy.
[1] https://github.com/binwiederhier/ntfy