Thank you for posting a review of your experience. My experience is that lines like Carnival and NCL attract more family cruisers because the baseline price is budget-friendly. If you want to avoid lots of little ones, try cruises of 2 wks or longer duration on lines like Princess and Celebrity. I can't say there are no kids on these trips but there are definitely less of them.
As far as parents letting their kids run loose, that's a poor parenting problem, not a cruise line issue. No one should substitute for the parent in terms of supervising young ones. Cruising should not be seen as an excuse to not keep an eye on your children, especially the schoolagers who tend to run, rather than walk. Sorry if this irks a few parents reading this but your kids really aren't as cute as you think they are when they are disrupting someone else's vacation. :/