Here are 3 problems I see.
1) It seems to be too expensive. When we go to the store we only see the costs of the food we buy. We don't take into account the time and other expenses such as gas, wear and tear on the car and the frustration that goes along with getting the food. Show people that it really is not as expensive as it seem and people will be more willing to sign-up.
2) Lots of packaging material that ends up in the trash. Hard to see that stuff go in the dump every time a delivery comes. Delivery companies aren't taking this into account enough. Look at Apple, they make sure you know how environmentally responsible they are. It may not be 100% reality but they act as if it's true and convince the customer of it.
3) the hardest to overcome. People aren't used to getting food delivered. People's behavior can change but it's not going to happen in internet time but in people time. I'm thinking a generation or 2, 20-40 years. Look at internet retail, only now is it coming to fruition yet it's been around for at least 20 years.