In NYC, the elderly and disabled have no natural access to these kinds of services unless they live a block or two away from such an establishment, for the simple reason that hardly anyone living in NYC owns a car. Yes, they can take a cab, and that makes it feasible, but economically speaking, the most common outcome is these people are dependent on the bodega on their block to provide their food.
I live in the West Village and just got back from picking up my weekly farm delivery six blocks away. The vegetables were picked probably in the last 36 hours and are consistently the most delicious I've tasted, including compared to my parents' gardens, where I can eat them off the vine.
I walked to the pickup place and back in less time I've seen people wait in line, or even walk from their car to the entrance of a supermarket.
The elderly people (>75) I know don't often go to places like Home Depot. In Barcelona supermarkets will be within walking distance -- if I've found the correct area on Google Maps, there are at least 3 within 300 metres of each other.
http://gothamist.com/2016/10/04/pedestrian_killed_by_bus_dri...
The only things I've ever had delivered by car or truck are things for which I would need a car or truck to pick up (furniture, more bags of groceries than I can carry.)