The various farm or feed stores that sell chicks get them from commercial hatcheries that cater to that market or sell directly to the public. A lot of chicks are mailed directly to purchasers, some are trucked. One of these hatcheries may hatch around 80,00 to 100,000 chicks a week in season. I don't know how many of these hatcheries there are, but a lot. These are not the hatcheries that hatch the commercial egg layers or meat birds. One of those hatcheries might hatch 1,000,000 chicks a week year around. Again, there are several of those hatcheries. Many of these hatcheries are small family owned businesses, often second or third generation.
The hatcheries we use are for the mass market. They may have 20 roosters in a flock with 200 hens so mating is random. You are not going to get show quality birds from them. Breeders breeding for show put one specific rooster with specific hens carefully chosen as most likely to produce a show quality chicken. Even with the breeders carefully selecting who gets to breed with whom the vast majority of those chicks are not show quality. Some breeders say they can get one out of five chicks as show quality but others say they do well to get one out of 10 chicks to be show quality.
The birds we buy typically look like the breed they are supposed to be but they also typically have "flaws" that would get them disqualified in a show. They are typically productive, often laying ore eggs than the breed is supposed to.
There are local breeders. Each state has poultry shows and crown champions. You may not be able to find your breed and some of these breeding for show quality don't want to sell their chickens. They don't want the competition at the shows. Some will sell them, even choosing breeding trios for you, but the costs you pay a show quality breeder are tremendously higher than a hatchery chick.
Absolutely not. Many people on this forum breed their own chickens. Not all are breeding for show quality, many of us breed for better egg production or for meat. Some if us do it just for fun.