npub1eecxxz329puzck2jue8jdx3nv4jattnzm7d999kr2r3aja6wzvdqk7xp4f (npub1eec…xp4f) You are 100% correct.
In practice the impact of a well implemented, persistent TCP connection is insignificant compared to other things that drain your battery like screen time etc. At least insignificant enough that I consider talking about "destroying your battery" as framing.
I also believe that not every app developer should have to go through the process of "implementing it well" - so push definitively has it's place. But it is also not without alternatives.