I wish push notifications worked better. It's so hard for open source projects. Ideally, a client should be able to, in a standard way, tell a server where to send notifications, maybe provide a key as well, and that's it. No need to register at each individual phone manufacturer etc.
Yeah, push notifications are an absolute shitshow.
A standardised push notifications API where you could swap out providers would be such a breath of fresh air.
That being said, the two applications I run that are doing long-polling sockets (Conversations and K-9 Mail) don't really use a lot of power, according to the battery settings screen on my Lineage device