The problem with physical punishment isn't that physical punishment by itself is damaging. It is that there is no established way to physically discipline someone, or any kind of rule for parents to go by.
I believe there is a cutoff age for physical punishment, where it simply is no longer effective and leads to potential damage to someone. The whole idea of physical punishment is not to beat someone until they are black and blue, it is to establish the mentality that doing a certain action = physical discomfort.
Our bodies work this way all the time in the real world.. You don't carelessly play with electricity - why? Because you get shocked and it hurts like a bitch.
You don't carelessly slam cardoors shut, because if your hand gets stuck, that's going to hurt.. You don't touch hot, because it is going to burn you and that HURTS.
Pain is just as much a learning mechanism for our brains, as it is a warning system to flee danger. You learn not to do certain things because it will hurt, and as you get older you learn to make judgements about potential outcomes of situations that could be painful in the end.. Taking a huge jump on your bike, crossing the street without looking, etc.. Some of us like the risk while others learn that it is wise NOT to do something.
Physical punishment when applied properly, can work in the same way, as long as the goal of the punishment is understood by the parent. When you give a kid a few whacks on the bottom, or a quick slap to the face, your intention isn't to HURT them, it is to develop the idea that you made a bad choice.
Your back talk to your mom and she smacks you? You eventually reach a point where you stop back talking to her - as a little kid. When you become a teenager physical punishment should stop, and I think this is where most damage by abusive parents is done. Then other punishments need to be employed such as restricted privileges, loss of property, etc. A combination of light physical punishment (a slap), a loss of privileges and property, and then sitting down and talking about WHAT YOU DID, is the best way to discipline someone.. Not some pussy ass timeout.
Nobody talks to their kid after they smack around. That is where the discipline falls apart, because you are leaving it up to an immature and still developing mind to decide why they were hit and what they did wrong. That doesn't work on teenagers because of the volatility of emotions, and being at odds with your parents as you come into your own, etc. You just assume they beat you because they hate you, etc..
If I had a child and they ran out in front of traffic to go see their friend, I would give them a quick whooping on the ass, ground them for a day, and then sit down and tell them WHY I did it. Explain that they can't run out in front of the street because cars do not stop when they don't see you, and you could be hurt or killed and that would make me very sad.
If some elitist harvad psychologist wants to say I'm damaging my kid, they can go fuck themselves, really. That is another reason why these methods don't work. Parents always have these know it all white coats, telling them they don't know how to raise their kid, they are doing it wrong, they NEED to do it THIS way, and threaten them with shit like they are screwing up their kid forever.
You don't get a parent to discipline properly by telling them they fail as a parent. You suggest to them to try something else and see if they think it is working better, and make it clear you are not invading their space as a parent or trying to take over their job.