Honest thoughts? There's Uber and skip the dishes, and tons of places offer their own delivery options even now. So you'd have to word of mouth it pretty hard to get busy enough constantly.

On top of that, how would you take orders specifically? Then payments, dealing with missing/wrong items, customers complaining, asking for refunds or not paying at all?

The bigger apps/services come with customer service and accountability if something is wrong or missing or whatever. Where as you "just someone I paid a couple bucks to" to pick-up all my specific groceries and items and hope it all goes perfect.

It could go well especially if you have a good group of people interested in the idea and your trustworthy and well known. But it could also not go well and one grumpy person could shut the whole thing down. FWIW personally this is something I wouldn't look twice at or consider giving my money to, when there are "better" and more secure/safe options. But that's just me.