And it doesn't actually work reliably, at least on Android. My wife and I frequently don't get notifications from specific apps, only once we open them. My impression is that the platform just changes too frequently with regards of what you have to do to work well even when you're killed. Also, especially for push notifications, your now at the mercy of Googles service to delvier them to your app (not sure how the open source variants do it)
Same for us on our Grapheneos Pixels. Notification are a bit of a lottery. But we take that as a feature. People can call if there's an emergency.
UnifiedPush is an open source solution for push notifications that isn't tied to a particular service provider. A handful of apps support it.
There is also the problem, that some OEMs add their own "battery optimizations". If you simply don't run anything its indeed very battery efficient... Forcing push notifications through some central service has minimal benefits at best. Open source variants are forced to publish annoying persistent notifications and ask the user to flip some "battery optimization" toggle deep inside the settings to not get killed, of course this often enough changes with Android versions.