This reminds me of a trip maybe 5 years ago to New Zealand- There was a family of 5 at the ANZ Intl lounge in Auckland, and the agent was trying to refuse the family entry. I remember overhearing that they were paying J customers, all 5, but the kids were maybe 2, 4 and 5 years old, and running around the entrance. I went in, and don't remember seeing that family after that....
I usually don't mind kids on planes. I find the problem to be parents who, like you point out, refuse to control their children. Lots of times, it's kids standing on seats during take off, or sitting in the aisle, or sitting with one parent and HOWLING for the other- each of which can be controlled by the parent.