Earlier quoted context omitted.
Background tasks become essential as soon as you need your phone to be a data aggregator for external devices. As an example, if you monitor biomedical sensors on your body, the app needs a way to reliably run in the background without being shot down.
The sensors should store the information inside themselves and then sync with the mobile when I open the app. No need to have my mobile awake all the time for something like that.
- Data is needed for real time alerting features for the user (e.g. low blood glucose).
- Data needs to be uploaded to cloud services in real time so carers have access to that data so they can also be alerted.
Both of these requirements require timely access to data. A delay can mean the difference between no real impact and "this user is now in hospital".
I find it interesting how you can't expand your horizon to see that these features are useful to somebody that's not you.