My HE kid goes to Cubs, has music lessons, karate classes, a tutor for French. All the things his school attending friends do.
You know, the groups chosen by their parents. Because children who attend school have parents making choices for them too.
He has an older brother who didn't do Cubs, Karate etc. and does not see him as a breed apart. I didn't do DofE, but my child does not seem to regard me as being at all peculiar.
My husband and I both work. The children spend weeks away at camps, and visiting relatives, and one of them has an eye on going to boarding school at 11. None of them are at all inclined to attend the local schools day in day out until 11.
As for being 'streetwise', I take it you mean developing the ability to deal with brattish children?
Frightful children go to Cubs, attend HE organised activities, play in the local park etc. too. With our HE children, and their siblings. And my HE children are not any more inclined to spend time with those children than their school-attending peers are.
They can though, deal with such children safe in the knowledge that they won't have to spend the next 12 months eating lunch with them.