I’ve never come across a situation in my life when it’s useful to say “be careful”.
Mostly, people say it when you’re doing something potentially dangerous, in which case “being careful” is probably something you intend to do anyway. And indeed, shouting “be careful” at someone walking a tightrope may cause them to turn around to look at you whilst working out what you shouted causing them to lose their balance and fall off said tightrope.
I see this in the same category as saying “have a safe flight” to someone about to board a plane. Unless you’re saying it to the pilot, the person you’re talking to is unlikely to have much control over the safety of the flight, so why say it at all.
I guess it’s short hand for “I wish you a safe flight” and “be careful” is short hand for “I don’t want you to hurt yourself”.
But this doesn’t inject any “point” into saying it. Just because I know someone doesn’t want my plane to crash, I am not going to change my view of the flight or my behaviour on it. Neither would I do so if someone said to me “I hope your plane crashes” just as I was boarding. Neither is going to make any difference to whether the plane crashes or not.
So, be warned, if I’m ever doing anything risky or dangerous and you’re watching – don’t say “Be Careful”!