As long as your kids are well behaved, have a little bit of street smarts their will be no issue. I realize times have changed, I'm 60 and when I was 10-12 especially during the summer my friends and I would leave the house at 8am and wouldn't be back until dinner, we would travels miles.
The problem comes in I've have seen it first hand when you have groups of pre teens and teens who are bored and roaming the ships. Playing games in the stairwells, making a mess in the buffet and just being disrespectful to other passengers and the crew. On the other hand I've seen plenty of drunk, angry disrespectful adults who I would have loved to toss overboard