If all people felt that way no one would run drugstores, and there'd be ZERO plasters / bandaids available on the market.
"It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest." --Adam Smith
While it does seem weird that coaches and organizers of these events - and even the parents - don't carry first-aid stuff with them... do your local pharmacies/chemists' just hand out medical supplies if you walk in off the street?
Any business is required to have a first aid kit on site and render help when asked to. If you organize any sort of event it's even doubly true. Not to mention that any car is legally required to have first aid kit to pass its yearly technical inspection(this is in Poland). So in an emergency you can run into any shop or stop any car on the road and you should get whatever first aid kits come with.
Wow, that's pretty awesome. The car first aid kit is not a thing in America (at least, I've never heard of it - there may be regional regulations in the colder parts of the country), and I think that while businesses are required to have first aid kits, they only have to render aid in severe cases (e.g., I can't walk in and ask for a bandaid because I got a papercut.)
Well yes, when I said they have to help I meant more like an emergency, not a papercut - but I guess most people would be happy to give you a plaster(bandaid) anyway.
"It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest." --Adam Smith
...and thank goodness for that!