Broadcast TV had a very simple solution to this problem: Only air the not-for-kids stuff at times of the day when the kids are already asleep, i.e. late in the evening or at night.

It was still the job of the parents to set the bed times etc, but at least this was something the parents could actually control.

And for pay-per-view stations with actual heavily violent or pornographic content: Yes, they were absolutely age-gated, usually via a PIN.