I love watching TYT. We have a lot of differing views, but I always learn from you and never really disagree with you. This is one situation where I strongly disagree. You have only addressed a single corporal punishment scenario here and that scenario is indeed inappropriate. It is inappropriate to respond to a child with violence. That is a very damaging action that teaches them all the wrong things.
The scenario that I think is constructive and necessary is to use corporal punishment as an escalation option. When a child is knowingly choosing to do wrong, you need to have a punishment threshold that the child is not willing to cross. You need to clearly warn them of what punishment will come and explain to them, "now that I have threatened to whip you 1 time with a belt I have to do it or else I am a liar." The child then gets to make a choice. They are then empowered. They are not a victim. This should not be considered violence. If you do have to whip them, you then issue the next warning, "do it again and I will double it." You then repeat this until you reach the threshold the child is not willing to cross. At some point 1, 2, 4, 8, 16, 32 you will reach the threshold where the child is not willing to continue. I will add that if you have a child willing to go to 4, this is a really good time to teach them about the power of exponents! I've only had one event where my child chose to be whipped. They chose to stop at 2 when I explained how quickly it becomes 128 and 1024. (At different ages either 100 or 1000 seems like infinity.)
I would prefer to take something away from my children or leave whatever place we are at when they misbehave. But, there are times when that is not possible. You can't just leave the DMV when that is what they want anyway, or end a trip to Disney World because one of your children choses to enter a power struggle. Sometimes the only logical choice a child can make is to "make it stop." I hate that this is true, but it is true.
Finally I want to close with repeating that it is wrong to react to a child with violence and strike them without warning. Sure, most of our parents did it, but they were wrong and we should learn from it. We didn't deserve it. It is very dangerous to think you did. Because if you deserved violence, you think your parents were right to use violence, and therefore you are also right to use violence. You are not.