I'm in the UK so bear it in mind (might be a different cultural setting i guess).
My DDs are 6 and 2. My 6yo is and has mostly been very chatty, my 2yo so far is by comparison rather shy. I think kids don't read social cues well, and i think they KNOW they don't. Which is why some kids will chat to anyone without any apparent boundaries/filters (my eldest frequently started conversations with the addicts and prostitutes working near our home when i was a single parent, and it wasn't always wise of her or easy for me to extricate us!), and some won't chat to ANYONE, even people they've actually met and talked to before.
I cannot think of anywhere that adults would model what is been described as the normal or desirable behaviour between kids in playgrounds on this thread. There is nowhere where it is appropriate to walk up to a stranger who is not part of a group you might be with and say "Hi, my name is such-and-such, what's yours?", and nowhere where you would expect to get a positive (or even neutral) response 100% of the time if you did. Not the cinema, the bowling, the gym, the bus, nowhere i can think of. People DO greet and talk to one another, but usually to comment on something that is happening (you might say "wow, this bus has been stopped ages, do you think it's broken down?" but you wouldn't say "hi, we're on the bus with you today") or because you're somewhere with a shared interest (you might say "Hey, i'm Bec, i'm knitting a cardigan for my LO, due in January" at the stitch n bitch, you wouldn't say it to the lady behind you in the bank queue (unless she for some reason was ALSO knitting in the bank queue). Even when adults WANT to meet strangers they most often attend groups, classes or go to a singles night or speed dating even to do so (depending on what sort of thing they're looking for). Adults also often use alcohol as a social lubrication in situations where it is deemed appropriate to meet and greet total strangers to spend frivolous social time with.
So back to the kids. My 6yo just did her first year at school, she's really sociable and polite (and has been given 2 in-front-of-school callouts at assembly to be given "...is a good friend and has lovely manners" awards) BUT she has had MAJOR issues with another girl who just doesn't take no for an answer. This girl really likes DD, but she has no interest in whether DD feels like playing on a given day or not. She MUST play, because the other girl wants her to. The other girl is devastated when DD wants to play with one of her other friends (and we have a list of 9 "best" friends DD did this year spontaneously to show off her hand writing) and feels totally hurt and rejected and will scream "you're not my friend anymore" or "i'm so angry, you can't come to my birthday party" (they are 5 and 6 please bear in mind), something which kills DD, who might just have happened to want to play Tigers instead of Princesses that morning. She has spent many a night crying at how painful it is that this girl controls what she does and cries whenever DD tries to do what she wants to do, and we have been in and out of school talking to the head mistress and teachers to try to help them work it out (DD is not the only girl to have had these issues). She, my sociable 6yo, has even begun to ignore this girl at times, because once she says "hi" in the morning, literally immediately the other girl will take her hand and that is it for the day, if DD dares to speak to or play with anyone else there are fireworks.
This interaction has made my DD much more wary of talking to keen-seeming strangers, which is a shame on the one hand, i agree, but i also think it's something she needs to figure out. Sometimes it IS a bad idea to engage with every person who just comes wandering up to say Hi, and sometimes it isn't. I'm pretty sure it was only through a childhood of being ignored, pestered and making good friends that i figured that one out. When people are antisocial with my DD's i say "well maybe they just don't feel like talking today" "they're in a quiet mood", "maybe they're tired" "i don't know why they don't want to talk, they just don't feel like it"... I just make sure she knows it's not a rejection of HER but of social interaction with someone they don't know at all, it's nothing to do with her as a person. This perspective, for our family, is the healthiest.