Potential problems -- maybe flying is easier
I have no doubt that it would work on Mars -- Curiosity and others have proven that.
But I can think of a number of problems here on Earth that the Martian environment is free of:
- What's it going to do when there's 20 inches of snow on the ground? (That's ~60cm for those on the wrong side of the Pond.) That's when it would be REALLY nice to have groceries delivered.
- There are a lot of areas where there are no sidewalks. The bipedal crowd can navigate obstacles that 6 wheels cannot, and if they can only go "walking speed" on the paved road, they're gonna get run over.
- Sure, they may be able to snap photos of people "liberating" them, but that just means that the crooks will have to use disguises, like they do now to rob banks, etc.
- Across the street as I type this is an 8-story apartment building. It's going to need some way of pushing the button to get to, say, the 6th floor. Previous commenters have talked about a mast -- maybe it could do multiple duty, and be used to push the elevator button (or, for that matter, the door bell upon arrival, or knock on the door the way the UPS guy does at my house). I'd be inclined to make the mast retractable, though.
Some of these problems/hazards go away for the flying delivery drones, though not all of them do.