I'm not about to force a mutt down anyone's throat if they like a specific breed. Personally, I am a devoted German Shepherd lover. I have one pure bred (with papers) and one mix. Both have typical GSD problems - allergies, arthritis, nerves - though the health problems we've experienced with our PB are definitely more severe. That said, both were rescues, one an owner surrender to a shelter and one a stray to shelter. I've worked with multiple rescues and fostered many, many pure bred dogs who were perfectly fine, but were given up because owners had no idea what they were signing up for.
It's good to know about what health and behavioral quirks might come along with a dog, beyond the traits that attracted you to them in the first place.
For instance - the general "OCD" tendencies and separation anxiety issues common in GSDs are too much for some people, but part of what endears the breed to me. Sometimes people do purchase dogs from breeders because they are looking for something in particular. Any REPUTABLE breeder will ensure you understand what you're getting into before they let you go home with one of their puppies, the same as most rescues and shelters will. Some even require you to sign contracts agreeing to meet specific care and food-quality/type requirements.
French bulldogs rank as one of my favorite breeds, however they are stubborn, difficult to train, extremely sensitive to heat and over-activity, prone to a variety of health issues because of their facial structure and their dwarfed stature (skin infections, breathing problems, heart issues, just to name a few) and many report that house training them is a lost cause. That said, I've been beaten (just barely) by a Frenchie and her handler in a Rally obedience competition (the mistake was mine, not my dog's).
Boston terriers, also adorable, are incredibly feisty and can develop severe behavioral issues if not treated with the kind of care and respect most reserve only for larger breeds (this goes for ANY terrier). I've taught puppy classes where two pint-size terriers made it their life's mission to unleash a reign of terror on a pair of Great Pyrenees pups. Without the training they received early on, those dogs would've become the little "ankle biters" so many of us would love to drop kick.