I remember being at the kid's museum and they have some enormous slides. DD was going down one, and there was a kid wanting to go up. I said "Hey S hang on a sec....." just waiting for the kid to get out of the way, and he did. Well then the mother had to do her "thing." She ended up telling her ds he must use his words and say sorry to my dd. SHe expected my dd to wait there while he threw a fit not wanting to. I just made a silly comment and told dd we should go up the slide again. She actually told me she needed her ds to use his nice words to appologize. I was like gee, well it doesn't look like he's going to and my dd wants to just go slide, and so we did. It was ridiculous. I'm fine with getting involved if it's necessary, like two kids fighting or something but that has never happened to me. My kids tend to be aware of others and not cause issues like that and I usually let kids work it out on their own. And the poor kid didn't even do anything in the first place. It was so odd. What I really wanted to say was "dd now we have to use our naughty words and tell her to eff off." But I smiled instead and went on playing. I don't know why parents can't just sit aside until they start throwing punches. Kids really ARE able to work out more on their own given the chance.
As far as shoes though we have to wear them. Playgrounds here have wood chips and it only takes one foot full of slivers to not do it again.