Everything you describe is how this works in much of the world, except remove the wheels.

The station near my work has three "supermarkets" within 50m of the entrance, catering to three different price brackets. There's nowhere to park, they sell very little other than food[1], and they only provide baskets -- they don't expect people to buy more than they can fit on a bicycle. They're open every day, from 7-22.

[1] They sell detergents and so on, but you can't buy a TV or a pair of jeans, or a huge box of anything.