Nitpick: background processing doesn't generally kill battery life because the platform API's provide guardrails around how long/frequent you can run, and batches as many wakeups together as possible. You essentially have a runtime budget you deplete as you run.

That said, you're right that most apps dont truly take advantage of background processing. What you have to understand is that the lack of background processing is what keeps notifications unsupported on iOS. Not only can you not support push messaging natively, but you can't _replicate_ a push messaging system either because there's no way to run code when your webpage/PWA isn't in the foreground.