It's a cute idea, but I don't really see it working in the real world. Every way I look at it, I think it would cost more money than it would make.
Day-old chicks weigh next to nothing; shipping them is relatively cheap (no pun intended!). By the time a rabbit is old enough to wean, it weighs a fair percentage of its adult weight, and is much more expensive to ship simply because of the weight.
The sheer volume that hatcheries manage makes the process itself relatively inexpensive. Hens can be kept in large groups, they will lay on an almost daily basis. The incubator is expensive, but the eggs only require minimal monitoring while incubating. A rabbit doe must be kept alone, only produces a litter after 4+ weeks' gestation, and she then has to care for her litter for a minimum of another 4 weeks (assuming that the animals can sustain a commercial pace). At best, a doe in heavy production is putting out maybe 6-8 kits in a little over a month. Most people don't wean until later because bunnies can be fragile at that age, if you were shipping 4-week olds you would probably run into pretty high losses. Litter sizes are unpredictable, and you have just as much time invested at kindling in a litter that is lost as in one that is alive and of good size. Some people do keep rabbit "colonies," but they still require careful monitoring to make sure all animals are healthy and not being over-worked. Production from a colony-type breeding operation is sporadic, but the people who do it don't mind, as volume and predictability aren't things they worry about.
Not many people would want several rabbits at one time. People interested in rabbits as pets would only want one or maybe a couple; babies that have had lots of handling make far better pets. Those who would want several at once would most likely be looking for meat production, and wouldn't want to pay the high cost of shipping that many animals just to slaughter them a few weeks later. Pet shops might be interested in buying smaller breeds, but many already have rabbit "puppy mills" that they buy from. If you were selling on that scale, you would need to get a license and meet several federal regulations to maintain that license, which can get expensive again.