The question of breeding always opens a can of worms in any pet species. I worked at a shelter in college that averaged 700-900 admissions a month and less than 100 adoptions (dog and cats only), that's pretty brutal math. I have seen the neglect that random breeding and the closure of horse slaughter plants has had on the equine industry. In our area, we have seen literally hundreds of horses dumped out in various locations to fend for themselves - many of those die of starvation, illness or injuries. The high price of hay coupled with the lack of outlet for unwanted horses (no horse slaughter means $100 to 200 to euthanize and another $100 to $150 to haul off the body if you don't want to shoot them and haul them off yourself - grim picture but it's the truth) has led to numerous starvation cases. We don't seem to have a problem with guinea pig overpopulation in our area - I had to spend a lot of time looking (months) to find my two girls to adopt instead of buying pigs from a pet store. However, the local classifieds are full of ferrets, sugar gliders and hedgehogs that are no longer wanted.
In spite of this, I am not 100% opposed to breeding animals when there is a basis for genetic improvement - we have come a long way in reducing inherited disease in dogs with genetic testing and careful breeding. Horses can be bred for better perfomance, increased trainability and better health. In cattle, swine, sheep and goats we select for both health and perfomance traits that are important for food production and animal welfare. I do think that anyone who decides to breed any animal should be trying to improve the species; and not just for them to look pretty in a show - "halter" classes in horses and conformation classes in dog shows often promote type extremes that do not always promote healthy animals. That being said, there are no DNA tests in guinea pigs that will help you select animals with decreased risk of cystic ovaries, URI, or bladder stones. And, at this time, there seems to be more random breeding happening then there are homes available. If the tables should turn and there are good homes for all piggies, then I think an effort should be made to identify traits that could be selected for to improve overall health.