When I was younger, I accidentally spilled Tabasco sauce into my drink and sipped from it. I thought I'd been poisoned.
I cannot regard kindly a parent who would do that on purpose to their child as a means of punishment.
I do agree with you, however, that unless you see a child being beaten and/or see bruises, CPS can't do much. That allows a lot of parents to skate under the radar, unfortunately.
I like your de-escalation advice, to help the parent feel less stressed or shamed in public. I remember hearing that that is how salespeople in the Middle East handle a Karen. They fuss over her and give her what she really wants, which is attention and sympathy, which calms the person down.