They are a breed that people steer clear of because of the risk of death in hot weather or hot climates. As Jo already mentioned, rats regulate their body temperature through their tails, actually up to 75% of it, and they can easily die of heat stroke under certain circumstances.
You have to be very experienced with breeding them, and truly know what you're doing, because you are basically breeding a rat with an underdeveloped spine. Babies can be born without most of their spines and have to be destroyed. Only one of the parents can be tailless, and it can only be one sex (I think the mother can be tailless and the father tailed) or you can have a disaster on your hands with the babies having to be destroyed. With only one parent tailless, you are going to get only a few tailless in a litter and that is where disreputable breeders do things like cut the other rats tails off to satisfy the number of reservations they have. There was a very awful breeder, up here in Canada, that was docking the baby rats tails and trying to sell them as tailless and it made quite a uproar in the rat community when she was caught. You have to be careful about things like that.
I have only heard of one breeder, with a decent reputation, in the US taking it on and I don't know if they do anymore.
In my opinion, breeding for that type of detrimental deformity should be criminal, I don't know why people would want to support that kind of animal breeding. Coat types and ear placement don't come with the same type of health concerns, and that is why they are more acceptable mutations, but a non developed spine is a whole different ballgame. It is the same with any high white breeding too, it is a detrimental mutation where the nerves on the spine are not developed properly.
Editing this to add that when I refer to coat types the exception is hairless rats which do suffer health concerns, by coat types I am referring to things like rex and satin and whatnot.
But, I am against any breeding of anything, so I consider myself biased.