Have you read my reply to pysc? I don't think you can 'get out of the game' of punishment. The fact is that you will punish people you are in close relationship to whether you like it or not. Even a frown or silence can be punishment and these sorts of things are not always under voluntary control.
I agree that the development of the parent is the key to reducing this. But note that development and learning themselves require peace and keeping the peace is a function of authority, both in families and in wider society. (This is not to be confused with authority in knowledge, which is irrational.)
My guess is that you saw punishment where it was excessive. This is a symptom of that lack of control at a deeper level. But control comes from self-awareness; removing authority would only make matters matters worse. Parents who try to be 'equals, as much as possible' will grow to dislike those they are responsible for and will periodically lash out in an uncontrolled manner. Literally so in some cases. Conversely, kids will willingly endure any punishment or chore in order to restore emotional connection to their parents.
Yes and because children are people rather than intellectual abstractions they need authority (not domineering but authority backed up by force nonetheless). A developing mind is like a nation, with many strands. I live in a relatively peaceful and advanced country but I know that if the police had their weapons and handcuffs taken away tomorrow then evil strands would quickly rise up and destroy everything.
Honestly, I suspect you'd probably like them. The fact is that trying to apply any parenting philosophy, however false, is on average going to be an improvement over current parenting. Children are starving for attention and interaction with adults. But parental attention is elsewhere, despite the fact that being with children is about the most fun and satisfying thing there is.
The point of punishing isn't to help with learning, it's to restore the emotional connection between parent and child by stopping the parent from hating the child. As Jordan Peterson put it: 'Don't let your kids do anything that makes you dislike them'. (He said this because he knows that people who dislike others work against them whether they realise it or not.)
The arguments against punishments tend to focus on severity, particularly if physical violence is involved. But the stronger the existing connection between parent and child, the milder the punishment need be. If it is strong even a frown might suffice.
I agree that the development of the parent is the key to reducing this. But note that development and learning themselves require peace and keeping the peace is a function of authority, both in families and in wider society. (This is not to be confused with authority in knowledge, which is irrational.)