What about when the phone locks? My phone is set to autolock after 1 minute. Leaving an app open just to receive notifications seems like a waste of battery.
If your phone is locked you will most likely not get the notifications, it just depends on the app. I do agree it can waste battery.
It's important to remember this is only a concern on non-free apps. The FOSS apps have very low power background services that check for notifications without the app running.
I use /e/os. It is based on LineageOS, is completely de-googled and has MicroG integrated. MicroG means push notifications with apps like WhatsApp will work. https://e.foundation/