I think it's the false sense of security being on a ship has. Especially on a Disney ship. After all, what can happen, we're all good people, aren't we?
And no one can get away on a ship, so they won't do anything wrong.
See, now I don't think it's this at all.
As a Mom, when I think of going out somewhere without my children for an adult evening at a restaurant, etc. I figure I will just leave my kids (DS15 and DD12) at home. I will either cook dinner for them or have them make themselves dinner (frozen pizza, warm up leftovers, whatever). They no longer need a babysitter as they are both old enough (and mature, responsible) to be left home without me.
But I would never send them out with money to a restaurant of their own while I dined at a different restaurant by myself. Not because I was worried about safety, but because logistically, it's dumb. They don't drive yet, so I'd have to drop them off and pick them up. Plus, there is free food at home, why would I pay for a restaurant for them?
On the cruise ship, there is no "home" with a kitchen and frozen pizza. So, in my mind here are my options: order room service and stay in the room, or go to the tween/teen clubs. But if going to the clubs is the choice, where would they eat? I guess counter service would work, but they are still dining without a parent that way. I suppose to some families another option is go to the MDR and then walk yourself to the room or the club.
What I'm saying is that I think it's more a logistical thing why people don't just send their kids to a restaurant without a parent when on dry land, as opposed to on a cruise, and not so much a safety issue, or a feeling of being safer on the ship. (This is a response to justmestace's question)
I think there are dangers anywhere on the cruise, as in our every day lives. I think children need to be taught about them as a part of growing up and gaining independance. Ship or no ship.
As for me and my kids on our 9/1 cruise (our first), I did not book Palo or Remy. I'm a single Mom and am viewing this as a family vacation where we spend time together, dinner especially. Maybe on the next cruise........