> What I don't understand is why DD gets any cut of the store's profit. They should be paying retail like anyone else, and their customer paying for the delivery costs.

It's a finder's fee, a very old and ordinary concept in business. The more sales you can bring to a company (or could divert to competitors), the more skin in the game you have. That's not to say I think these companies aren't in some ways anticompetitive to the detriment of merchants and DIY shoppers.