Oh, this one's interesting.
I'd have to say that with mammals, it's not that 100% of the offspring produced are "nice," rather, it's that gradually the amount of "mean" offspring are reduced. The reason animals are aggressive is because they have genes that cause them to be so for survival requirements--an animal that's too docile quickly gets picked off by predators. Therefore, it might be looked at as not having "nice" genes but malfunctioning "mean" genes.
If the malfunctioning mean genes keep getting passed down generation by generation by generation until that's all there is, what you may end up with is a completely docile reptile. But it wouldn't be an animal that has affection, like a cat or a dog, since you'd have to have basic nurturing and social gene sequences for that. It may just end up being a snake that simply doesn't know how to fear which in turn doesn't bite, or hiss, or musk.
Some dogs, were selectively bred to remain neonatal, if you look at adult wolves, they don't keep the puppy tendencies of constantly trying to please. Some dogs had minimal amounts of tweaking in this aspect and we call them "aloof" or "cat-like" even though in reality they're just normal, like wild dogs. This is why dingos are considered on the list of dangerous animals.
Cats, however much they're considered "wild" really aren't as undomesticated as some people think--nab a kitten from a feral litter and it will still become tame in a matter of weeks even though by logic, a wild animal should not recognize people as their "family." Cats are also not social animals, coming together only to breed and for a little while after they're born--yet they actively seek human attention. I always found this fascinating.
A lion and tiger and cougar may still contemplate eating you if it gets hungry enough.
Both of these animals somehow lost their fear of humans and, in the process, truly became pets.
(btw, this is all speculative, as reptiles aren't mammals)