Sorry, if your child is THAT allergic then "uncontrolled" spaces need to be off-limits/monitored for you, not the whole world. I mean, squirrels run around playgrounds and they eat nuts, birds drop nuts and seeds...
The problem is, there's no boundary between "THAT allergic" and "just a little allergic" for many people. Previous reactions don't necessarily predict future reactions - so if you know you're allergic to peanuts and you've had two mild-to-moderate reactions in the past, you don't know whether the third reaction will be anaphylaxis or whether it will just be a bit of a rash. A huge percentage of kids nowadays have food allergies (10%, according to the article), and there's no "little bit" when it comes to unknown reactions. It's a shame, because peanuts are such a good and cheap source of protein, but (as I mentioned upthread) I do think it's polite to moderate your peanut-germ-spreading ability when you're likely to be around children.
re: the bolded: Yes, this. It's definitely considerate and kind for parents of non-allergic children try their best not to spread serious allergens around kid-centric areas. The posted article also contains good info about how to do so (wipes instead of hand sanitizer, etc).
However, if (general) you don't have a kid with those kinds of allergies, you're probably not going to be nearly as vigilant or thorough because it's just not something you deal with or think about regularly. If I had a peanut-allergic child, I would not risk his life on "I don't see anyone eating peanuts or any peanut butter on the monkey bars, so we're safe." Who knows if the kid in the sandbox ate PB crackers before coming to the playground and mom didn't wash his hands properly, or he still has some crumbs on his shirt or PB on his breath? Or if the kid is a little older and got herself a granola bar mom didn't know about, so mom didn't know she needed to wipe hands, change shirt, rinse mouth, etc. Ultimately, it's still on the parents of the allergic child to be extra vigilant simply because they are the only ones who know best how to keep their child safe.