I've wondered this myself after reading Bradshaw's book on the domestication & psychology of cats, _Cat Sense_, where he points out that not only are cats not nearly as well domesticated as dogs and this seems to be the root of a lot of cat problems (such as the urinary idiopathic cystitis which nearly killed my cat last year, or the cat bites which are extremely dangerous and send countless people to the ER with blood infections, including my grandmother), they also are probably de-domesticating as cat reproduction is increasingly carried out only by feral strays. Cat personality and personableness definitely are genetically influenced, and this has been demonstrated by the usual methods like crossfostering (the offspring of feral fathers are less friendly even when raised by friendly mothers with zero contact with the father).
I'm not sure why, but it seems to be that most people don't regard it as a problem that can be affected, it's "just how cats are", and the scattershot cat breeders are almost all entirely obsessed with coat color/appearance and to a very limited extent, the worst inherited diseases. In addition, there is an incredible lack of cat research compared to dog research, despite being such a popular pet, which has even drawn comment from outsiders: https://www.nytimes.com/2018/02/26/science/dog-science-cats....
(My favorite example of this: for 60 years, if you asked any reference source like Wikipedia about why some cats respond to catnip and others don't, you'd be told this is because catnip sensitivity is controlled by a single autosomal dominant gene, based on 1 small Boston cat colony pedigree done back in the '60s. Turns out this is entirely wrong, it's highly polygenic, but it took until 2011 for a grad student to demonstrate this, and it took another 6 years until I stumbled across her thesis and added it to Wikipedia.)
Not sure, but here are some thoughts: cats and dogs occupy different niches. Feral cats are mostly not a problem because they don’t prey on animals that humans depend on for food. I guess a cat could take down a chicken? It would probably be dangerous, though. Chickens are big. Feral dogs, on the other hand are a problem because they will eat animals that humans are raising for food. After all, there’s a reason wolves have been exterminated throughout most of Europe. So, that difference, combined with the fact that cats just aren’t very useful (they don’t protect or herd livestock and they’re not useful for hunting large game), means that there was never a historical reason to breed them.
Now as to why there hasn’t been a concerted effort to breed them as companion pets. I think the big reason here is that there is already an animal that is the same size as a cat, but extremely domesticated: small dogs! Animals as companions hasn’t been a widespread thing for very long. My guess is that, when that started being a thing, smaller dogs were much closer in evolutionary time than more dog-like cats. And I’m guessing the people who enjoy cats as pets now probably appreciate that they are less emotionally needy than dogs.
I can recommend "Veterinary Aspects of Feline Behavior" by Bonnie Beaver, DVM, to people who keep cats.
Even stray cats usually responds well to good care if you know what you're doing and have the endurance, skills and resources to do so.
Or: you don't need to do this with dogs—at least the breeds people actually keep as pets—because [those breeds of] dogs have been bred for friendliness.
Most popular breeds for pets bite.
Given that "cats are assholes" is a common aphorism, this doesn't say much. (I get that you mean that they're friendlier than cats at their best, but few cats friendly a majority of the time.)
Tangent: why hasn't there been a breeding program to make domestic cats... more domesticated (i.e. friendlier)?