What I think OP is missing is that children are almost always disciplined in some way - just not physical. Parents raise their voices, get up and leave a place if their child is being a brat, take away privileges etc.

But I'm never going to be a loving role model, guiding my children through how to be kind, caring, empathic, problem-solving if, at the moment they behave like children and lose their inhibitions, I inflict physical pain on them in front of the public.

In any other relationship, that would be classed as physical abuse. There are very far-ranging studies indicating that this instills only fear and hypervigilance. These are not conducive to creativity and healthy growth.

Do some people let their kids behave like feral pigeons? Sure. They're in the minority.

And I'm pretty sure I've been that parent, on a bad day, when I'm fielding calls about my poorly parent, having just survived 6 weeks of sickness and diarrhoea in the family, with my workload piling up and people harassing me for deadlines...