I used to breed cats, so I guess I can provide my response on that basis. I think that any breed that reinforces faults such as dwarfism, hairlessness or similar which, if nature were to take its course, would reduce the animal's survivability, should be actively discouraged (as indeed should be breeding for 'type' to the extent the animal's health is compromised).
The question of 'new breeds' is more complex. Arguably there are quite enough breeds to give any reasonable person a wide choice in terms of shape, colour, personality and the like, and I am concerned that many new breeds are catering to the 'pets as ornaments' crowd.
Up until recently I have been under the impression that Bengal Cats, for example, were banned in Australia, but I have discovered in the last couple of days that not only are they there, there are over 30 breeders on-line (which presumably does not include the smaller breeders). That a breed that was banned when I left five years ago has become so popular in such a short time that is warrants that level of exposure, is concerning. It suggests a whole heap of people 'jumping on the bandwagon' with little thought for the animal, its ultimate destination, or responsible ownership. BTW I adore Bengals and have passed up several opportunities to have one since here on the grounds I was concerned I would not be able to take it home with me, but that is by the way ...
If, before breeding, people could be required to undergo training and suitability asessment and licencing based on a high standard of animal welfare, then perhaps we would not have the problems we have with back-yard breeders and irresponsibly owners - it is the eternal question, really.