You hit the nail on the head. Behavior! Have a plan. Toys, coloring, snacks, even!
For the record I would not go to or not go to a restaurant based on whether children are allowed in or not. But we probably would not return if we had a bad experience.
That’s why the restaurant has an obligation to the other diners to insist on proper decorum in the restaurant. Restaurants throw out drunks who are disturbing other diners. Its an unpleasant task but a necessary one. The same should be true of any diners causing a disruption.
If a particular restaurant is having enough problems will unruly children I can see why they would have the temptation to institute age limits. It would be better to just quietly ask a group to leave but the restaurant gets to decide if there have been too many disruptive occasions with children and they are tired of dealing with it. I think its like throwing the baby out with the bathwater because many customer families are courteous and responsible diners.