Well, I'm in the U.S. Where will you be offering this service?
Though I suspect you'll go through the technical efforts necessary to get this running and then a few weeks or months later you shut it down because you are operating as a money transmitter, according to FinCEN.
But there are multiple grocery options available today and I don't use them. The most recent service I looked at wouldn't work because I couldn't be sure I would be around during the delivery window. If they were to drop off and leave, I wouldn't want to order anything refrigerated. Another service I was going to order from, Alice.com, would ship the items to me, but again but again -- the logistics of the delivery getting dropped off (and possibly disappearing thanks to not having a halfway secure method for accepting delivery (e.g., a porch), that just isn't something I'm that anxious to use.
But I see the delivery trucks out and about, so there are others that do use these services. And the order sizes are enough to where there's almost always a few dollars per order going to VISA/MC.
Sorry, I should've mentioned that in the OP. It's the Australian supermarket Coles. They do both home delivery and pickup directly from a loading dock at the back of a few key big shops.
FinCEN doesn't have any jurisdiction here as far as I'm aware.