When I am at the park with my dc (6 and 3) I mostly just see children playing with their parents and not really mingling with each other unless they already know each other. My dd has tried a few times to talk to other children at the park and they just stare at her or run off. She is also shy about talking to new children and both DC want us to play with them all the time at the park, just like I see the other parents doing.
I'm not a confident person but I used to love making friends with other children at parks (well usually pub beer gardens in my childhood!) And especially on holiday, my brother and I would just go up to people and become friends for the rest of the holiday! We are going away soon and I would love that for her but it just never seems to happen and if she ever does interact with other children it feels like I or the other parents always have to intervene in some way which my parents never did. If we argued as kids we just had to work it out and not come crying to them every five minutes!
This isn't to say that I don't want to spend time with my kids, but I just want them to be able to play more with other children and for parents to actually sit and talk to each other and finish a sentence!