This is an interesting thread - I only just came across it. I definitely agree an adults-only area should be enforced. I'd be extremely peeved if I chose a ship because of the nice "adults only" area and then found that it was not in fact adults only. Good kids are noisy and boisterous and run around shouting and splashing and having fun, and I think that should be encouraged (in the appropriate places eg family pool). A few teens quietly sunning themselves in the adult area wouldn't bother me - if they're behaving like adults that's fine by me. Likewise I see babes-in-arms as an extension of their parents, I don't have a problem with them in any adult area so long as the parent takes them out if they are crying and can't be comforted.
Our kids are pretty much grown up now, so we can take them anywhere. But when they were younger, we had different types of holidays. A family holiday revolved around the kids - what they'd enjoy, what would be educational experiences for them - we planned the itinerary around them and gave them lots of attention and supervised them at all times.
If we wanted to relax or do stuff they wouldn't enjoy, they didn't come! We would take child-free breaks leaving them with Grandma, and we'd hire a nanny to help her if it was for very long or when the kids were toddlers and more difficult to manage. Or sometimes each of us would have a break on our own or with friends while the other stayed home to look after the kids. If we'd had nobody we could trust to leave the kids with we might have gone to a resort with a good kids' club to get some down-time together.
Ironically, as the kids have gotten older we could easily go away without them, but we usually choose not to as it's more fun having them along.
I don't think it's fair to take kids on a holiday if we're planning on ignoring them, and then moan when they misbehave.