Surely laughing when your child falls over leads to them enjoying others misfortunes

No it’s a cognitive framing thing. The concept is to make a toddlers tumbles into not a big deal for them. I think it is also in part an overreaction to the common “oh you poor baby” response which is thought to encourage children to be upset when they fall. I favor the Montessori guide approach of observing|ignoring and giving a kid a chance to make up their own mind to ask for help or deal with it themselves. The optimal approach probably depends on the kid.

I think you're assuming the laughter is at the child, not with the child. It's laughing about a mistake because that's what makes us human.

Do children understand that nuance? I would have thought they would associate people falling with laughing

When I pick up my children from a small fall, and I laugh belittling the hit, they do not feel mocked at, instead laughing with me. I think the kind of insecurity that makes you suspect that people are laughing at you comes later - and if you don't have crappy parents you don't even come close to suspecting that your parents might be laughing at you...

Obviously you don't laugh with big falls and broken arms.

But when your children are with their friends, and their friends fall over, do they laugh? Maybe their friends aren't as confident

They are still very young.

But from my own childhood I can remember that kids are not subtle - if they are mocking you, you will know (names, finger-pointing, jokes, etc.). Whereas if a friend laughs with you about a silly fall, you get a completely different kind of scenario played out.

Coming back to your initial point, and being blunt: showing your children that clumsy falls can be funny, and not to panic about them, does not increase their cruelty towards other kids.

They aren't dogs. They understand a lot more than you would expect.

Very young children mirror the emotions of their caregivers. Generally if you laugh they will think that it's time to laugh, if you are concerned they will think it's time for them to be concerned. Very young children don't really understand what to do when they are concerned, and so they cry hoping that their caregivers will focus on them and make things better.

Yeah, I think there's a middle ground between teaching a child to laugh at injuries and immediately having a protective, sensitive reaction. Personally, I tell my son, "You okay, bud?" in a positive tone and wait to see whether he needs comfort or is ready to get back to playing.

Everyone parents differently. I would be interested to see which culture the "laughing" reaction parents come from.