I've studied Martial Arts for about 12 years. You're totally right. It takes years of training to learn how to properly throw a punch such that you harm your opponent and do not break your own hand.
And part of that is not attacking targets where you're likely to significantly injure yourself as well as your opponent. There's a lot to be said for not punching someone in the jaw.
It is still possible to knock someone out with a slap. Some bouncers in the UK recommend it as a) it doesn't hurt your hand so much and b) telling the police you just slapped someone doesn't sound so bad. Plenty of videos on youtube of people being knocked out with a slap.
being knocked out is related to the brain hitting the walls of the skull, it has very little to do with what caused that. Slap, Fist, head-butt, concrete, car crash etc.
But I was responding to the claim slapping is equivalent to punching.
Depends on the goal. You're right about it being less likely to break a bone (on the target) or cause bleeding (again, on the target), but a solid slap will cause similar secondary impacts (brain hitting the skull)
I'll take a KO after some body shots and two working hands over a bloodied up opponent and a broken hand. There are much better tools to use against a skull, like elbows (less delicate than hands), but you need to account for range and movement.
There are completely different mechanics in a slap though. With a punch you have different delivery options (looping vs linear vs uppercut etc) all of which affect the way in which the force is generated. With a slap you're pretty limited.
That said, getting slapped has a psychological effect you don't get from a punch, which can be exactly what you want.