5000 years isn't that long in evolutionary biology timescales. But culturally we do kinda like the usefulness of the smaller cats.
I would say that the cute cats are domesticated species, like many animals. So they wouldn't exist without humans, and it's in their benefit to behave to survive.
Interestingly enough, the genomes of wild forest cats and domestic cats have diverged FAR less than other domesticated animals such as dogs/sheep/etc. We domesticated other animals, but up until the 18th century or so I'd say it's more accurate to describe what we've done with cats as "co-evolution"
Cats are more "companion" rather than "domesticated" and (until recently) cats weren't bred for specific traits (and those now tend to be aesthetic choices rather than "practical" choices).
Compare this with dogs that are more of a "working animal." We've bread dogs to fill specific roles because they were larger to work with. If humanity had tried to find companionship in the mountain lion instead of Felis lybica (the wild cat).
I suspect part of the lack of range comes also from that the cats of size that don't eat us are not ones that can be crossbred with cats in the wild to introduce new useful genes. Trying to cross a domestic cat a wild cat doesn't produce a new cat that is useful in a new role ( https://en.wikipedia.org/wiki/Felid_hybrids#Confirmed_domest... ). Compare this with domestic dogs and the various wild dog species.
> The remarkable responsiveness of dog morphology to selection is a testament to the mutability of mammals. The genetic sources of this morphological variation are largely unknown, but some portion is due to tandem repeat length variation in genes involved in development. Previous analysis of tandem repeats in coding regions of developmental genes revealed fewer interruptions in repeat sequences in dogs than in the orthologous repeats in humans, as well as higher levels of polymorphism, but the fragmentary nature of the available dog genome sequence thwarted attempts to distinguish between locus-specific and genome-wide origins of this disparity. Using whole-genome analyses of the human and recently completed dog genomes, we show that dogs possess a genome-wide increase in the basal germ-line slippage mutation rate. Building on the approach that gave rise to the initial observation in dogs, we sequenced 55 coding repeat regions in 42 species representing 10 major carnivore clades and found that a genome-wide elevated slippage mutation rate is a derived character shared by diverse wild canids, distinguishing them from other Carnivora. A similarly heightened slippage profile was also detected in rodents, another taxon exhibiting high diversity and rapid evolvability. The correlation of enhanced slippage rates with major evolutionary radiations suggests that the possession of a "slippery" genome may bestow on some taxa greater potential for rapid evolutionary change.
I would say that the cute cats are domesticated species, like many animals. So they wouldn't exist without humans, and it's in their benefit to behave to survive.