I don't know about UK-US, but I think I've noticed a difference between the UK and Germany in this respect: in the UK the sign tells people that something is dangerous and gives some hint of why; in Germany it just says "Verboten" with no mention of the danger, which in the UK would seem to be highly negligent and asking for legal trouble.
Something that injures a burglar could equally well injure a police officer, a fire fighter, a representative of the water company, ... it's amazing how many people can legally enter private property without the owner's permission. Of course one should be allowed to assume that such uninvited visitors are cautious professionals so you don't have to make everything childproof, but if you're aware of a serious danger yet can't be bothered to put up a warning sign ... you'd better have good insurance.
"it's amazing how many people can legally enter private property without the owner's permission"
Scotland has 'right to roam' so we can wander about pretty much anywhere (with a few sensible restrictions) and there are actually very few signs at dangerous spots - I can only think of a handful. The idea that you would go onto someone else's land, have an accident and then blame the landowner seems a very strange idea to me.
Something that injures a burglar could equally well injure a police officer, a fire fighter, a representative of the water company, ... it's amazing how many people can legally enter private property without the owner's permission. Of course one should be allowed to assume that such uninvited visitors are cautious professionals so you don't have to make everything childproof, but if you're aware of a serious danger yet can't be bothered to put up a warning sign ... you'd better have good insurance.