How does that work? Naively, I'd expect that the more expensive labour is, the more disposable income labourers should have available to spend paying other labourers to deliver food, so it all balances out. It's at least not obvious that food delivery would be less viable in the US than, say, China or India, where labour is cheaper but customers also have less buying power.
The extremely poor live in huts/have no expectations of moving up/have no education with which they can do things other than manual labor.
Although, even in India, the cost for cooks/maids/drivers/farm workers has exploded since the 90s. Many families that used to be able to afford them, cannot anymore. But that does not mean the cook/maid/driver can afford their own maid. It just means they now have the ability to eat at a restaurant once a month or buy a smartphone.
But mostly, people are living so close to each other than delivery is much cheaper. It costs a minimum $0.60 plus labor costs per minute of driving in the US. Cost to run a 15 min errand is $7+, and that is excluding the person’s time and effort.