Wow...did you ever hit on a hot topic!

How I feel about is this:
First off, they are not "breeds." A breed has a set standard. Designer dogs/mixes/cross breeds/mutts, take your pick are not recognized "breeds."
Health issues are not a result of a breed being popular and overbred, it's a result of indiscriminate breeding practices. People not taking the time to select quality stock, take the proper precautions to test their dogs first, and not taking the steps needed to ensure that genetic defects are not being passed on to generations. Health issues are not eliminated by mixing breeds...in fact, just the opposite could occur.
"Teacup" is basically taboo in regards to any breed. Breeders claiming such are usually the type people are advised to avoid. None of the breeds classified as toys (Yorkie, Chis, Maltese, Shih Tzus, etc) have subcategory in the standard based on the size of the dog. Furthermore, ethical breeders strive to achieve the standard, not to produce extremely small dogs.
I do not support purposely breeding mutts. Really, what is the point? To get cute little puppies? There are plenty of those in shelters that need homes. There's no goal standard to aim for, and it opens up a wide variety of possible problems. Is it done for the fun of the experience? Any experience breeder can tell you that it's not only costly, but not all "fun" and games.
IMO, it's nothing more than a fad and many are jumping at the chance to supply the current demand with no regard for the bigger picture and the best interest of the dogs in the long run. It's an easy way out...no specific health test to worry about, and no standard to judge the quality of the dogs you produce by. It's funny, but questions as simple as "why do it" and "what are you trying to achieve"
should be easy ones to answer.
Understand, I in no way think that cross bred dogs are any "lesser" than purebred dogs. I have owned my fair share of mutts and wouldn't have traded them for anything. However, I don't think that they should be bred purposely.
So, I'm sure that opinions vary, and that is fine and well, but that is how
I personally feel about the subject.