Well, traditionally a breed would be made to fill a need. The dogs that performed that need best (tracking, pulling, guarding sheep, coursing, etc) would be bred, and those that didn't or couldn't performed were culled (killed). This is why you see a lot of similar types of dogs appearing in wildly different parts of the world. The native Norwegian scenthound breeds (look up Halden hound or Dunker if you're interested) look very similar to hound breeds originating in the UK, in America, and in other parts of the world. You look at them and say "oh, yes, that is a hound" even though those breeding them weren't deliberately breeding for appearance. Selecting for certain performance abilities seems to, in many cases, also select for a certain look.
Sometimes appearance was taken into account (and size certainly was), but very often it was much, much less important than whether the dog could work as intended. In more modern times, it's become more common to breed with appearance in mind (eg the Leonberger being bred to look lion-like), but you don't see that very often with the very old breeds of dogs. Very modern breeds (Miniature American Shepherd, Silken Windhound, Alaskan Klee Kai, etc) are also bred with a goal in mind, but we have very different needs these days than we once did, and hard culling is no longer considered ethical in many circles, so development can be relatively slow and you see relatively more breeds being developed with emphasis on looks and being good companions for modern dog owners. We also have way more tools concerning genetic health, and so a lot of people serious about developing new breeds these days make full use of these tests and scans to ensure they're creating a healthy and sound dog.
But the concepts of recognized breeds, breed standards, and breed clubs is really quite recent, as is the emphasis on breed purity and closed stud books. For a dog to be recognized as a breed by organizations like the AKC, it at the very least needs to have a breed standard and be able to breed true - by which I mean that when two dogs of the breed mate, all their puppies also look and act like breed standard describes, give or take some minor deviations. There's more to it than that, but without a standard and breeding true, you're not going to get anything recognized.
Because of this, many cross-breeds like goldendoodles, cockapoos, etc. will never be considered a genuine breed by the AKC, FCI, and other reputable kennel clubs. For better or for worse. This is because most breeders of these mixes are constantly breeding back to the parent breeds, or breeding exclusively first generation crosses (golden x poodle instead of goldendoodle x goldendoodle). This can be because the litters of two mixes can have an extremely wide range in looks, size, and temperament of the pups. IE, they don't breed true.
Programs like the Australian Labradoodle are trying to breed for a single, consistent look and temperament, and trying to set that type in their lines (turn them into a recognized breed, essentially), but that is the extreme minority of cross-bred breeders. It takes a ton of work and a ton of dogs you have to find homes for because they just don't match the standard you're aiming for. It takes many, many generations and, like most breeding, isn't profitable if you're being ethical about it. And unfortunately many - not all! - breeders who breed cross-breeds are primarily focused on income, and tend to skip important steps like in-depth health tests, vetting puppy buyers carefully, or quality puppy raising/socialization programs, so they're simply not motivated to create a whole new breed.
For the record, I'm not down on crossbreeds. I care a lot more about whether someone is breeding ethically and responsibly than whether they're breeding a purebred or mixes, and I think a lot of the breed purity/closed stud books stuff is extremely short-sighted and harmful to all breeds in the long run. There's some really excellent breeders out there producing mixes for companionship or sports, but there's also so, so many people who cut corners that it's frustrating.
I am also NOT a breeder, just an enthusiast, so if I've flubbed anything please let me know.