I think I went to sleep away camp starting at a very young age. I remember it was day camp for awhile, but I was super active in Cub Scouts and Boy Scouts, so I quickly started in on the week long camps.
Eventually I started going to Woodward every year for two weeks, and then got a job there (extreme sports camp in the middle of Amish country, PA).
When I have kids, as soon as they can walk they are going to adventure-oriented summer camps. Everything cool I enjoy started there- white water rafting, climbing, skiing, snowboarding, ropes courses, horse riding, go karts, etc.
I'll be sending my girls to overnight camps as soon as they're old enough for the reasons you listed. They'll get to do all that cool outdoors stuff that you can't really do in the city. For now, they do a couple of different day camps. This past summer they did a gymnastics camp, which they both loved. We're thinking about a horse riding camp this summer, which my wallet is already hating me for...
I've never really considered the networking aspects of camp. It seems very strange to think about for kids that age. Although I do have my kids in violin and dance throughout the school year, in part so that they are able to connect with other kids from families that have higher expectations for their children.
I grew up poor as shit, so all this is new to me. Haha.