John, you and I grew up in the age of Baby Boomers, and there were actually enough kids around at one time to form an impromptu team or battle sides. Nowadays, kids have play dates because there aren't enough kids around to do the fun, unplanned stuff. When most famiies have one, or maybe, two, kids, and homes are far apart, there just isn't the opportunity to do what we did back in the day.
Just because it's a play date doesn't mean you can't have fun. You can play with dolls (I assume girls still do) and make up their worlds, and an empty box or a trip to the basement can provide hours of imagination. If they're brave enough, parents can even let kids wander by themselves for a block or two.
I'm fortunate enough to live on a cul-de-sac where magically, families have two, or three, or even four kids, so there's always somebody around to have fun with. Play equipment permanently lives on the sidewalk, so there's something to grab, as long as you put it back. It's definitely more sanitized, but it's still fun.