I know that not all young adults act their age, but let's not stereo type... I was a very responsible young person (even before 18...) and was married and starting my family at 20. My husband and I always followed the rules, dress code, etc on our cruises and elsewhere!
However, I do agree parents need to keep their kids out of the adults only areas. I think this should include the dining room. If you know your children don't sit nicely for dinner, eat at the buffet or room service. My kids are 3 and 5 and I won't take them cruising until they can behave well enough. I have good kids, but I am not blind to their behavior. A formal dining room meal is too long for them yet.
If only the parents of the well behaved children let their kids in, no one would complain. But then they would attract more, so no kids means no kids. IMHO.