Yeah, about that. We run repair shops, and were approached by Favor (Postmates competitor) about doing this. We love Favor; they are local to us in Austin and we'd like to do more business with them.
The problem was insurance. Our insurance refused to cover it as the phone wouldn't be in our possession. And (at least at the time) Favor's insurance also was not covering if a phone was lost or stolen during a "run."
When it's a small food order (most of the food orders they run are around $20-$30, or even less), it's not the end of the world if something gets lost or stolen. It's a lot bigger deal if it's a $969 iPhone 7+. Even with a broken screen and iCloud locked, they're still (unfortunately) worth significant money on the black market.
As far as I know, no delivery company has overcome this hurdle.