Each breed has its traits.
Pit bulls were bred for fighting other dogs, not attacking people. That is a new thing with them due to the kinds of morons who misuse them and people who don't take adequate precautions with them.
Teddy Roosevelt had a "pit bull", so did "Buster Brown" and other people. Unless a dog is crazy, it can be socialized with people - with a few rare breeds excepted like the Fila.
I think you're mostly right and I can agree, but I wouldn't have put it that way... Pit Bulls were bred for dominance and aggression. "Competent" dog fighters and breeders don't get in trouble with them because they don't let them loose in the house, the dogs go from chain out to treadmill to fighting ring and back to chain out.
"Regular" people do let their dogs mingle with them, their families, and their other pets. A dog prone to attack other pets is NOT desirable. A dog prone to be dominant and aggressive is not good around children. Some people say "well they're only aggressive to dogs, not people" Well that's not really true for one... Dominance is dominance, the only difference between dog aggression and people aggression is where the dog sees you in the pecking order. But still... a dog who might kill another dog if it happens to get loose is a liability as a pet and not for the average dog owner. Lots of questionable people try to have pits go both ways... tough dog, but pet.... Even well-intentioned people try to put pit bulls in home situations and think they'll just forget all the traits it was born with. They don't.