This is a similar question to that raised by Denny in the in-breeding thread that is currently running. It may be that many of the crossbreeds out there originate either in bunny farms or by accidental breeding. The bunny farmed ones are not to keep the breed and maintain health but for cuteness and year round availability, therefore there may be faults in them that are not removed. The results of accidental breeding could be from siblings which as breeders state in the in-breeding thread should not be done as deformities are more likely to occur in these babies.
Therefore, buns of a standard size which are well bred would probably outlive many mutt buns.
I think the difference with dogs is that there are so many health issues that are intentionally bred into some breeds i.e. pugs, pekes etc. often struggle to breathe as their noses are too short, plus there are many puppy farms that mass produce popular pedigree breeds and therefore may not eliminate problems in that breed. Mongrels do not seem to have this type of health issues.
There used to be a feral cat group that lived in the grounds of where I work - they produced kittens and if these could be caught then they would be rehomed, many to people who worked here. These kittens did have many health problems and were often short lived. The company eventually paid for a spaying/neutering session and these cats have now died out.