Everyone will have a different opinion based upon what they see as the maturity, responsibility and comfort of their own kids at a given age and their comfort level in providing freedoms to their child . IMHO an 8 year old would be to young to wander an unknown space (or ship) on their own. A 10 year old may manage, but I would not let them loose until they had proven they know their way around, know whom to approach if having a question or issue and could demonstrate what to do in case of serious emergency that can arise on a cruise ship.
I don't believe anyone would give a young one freedom of a neighborhood having just moved in - I would apply the same logic to a young one on a ship.
Our 12 year old stuck close to us most of our first short cruise (learning about the space, what was available, where she could go) and was given some freedoms to explore (specific areas, going to specific places - like the tween club or meeting us at the restaurant because ready early). Eighteen mos later sailing the same class ship, she was given open freedom knowing the layout, where she was allowed, showing demonstrated maturity and always having a wave phone to both check-in and if need be, be reached.
I would have to agree with several PP's that the ships are by nature safer than the our communities as a whole (as the highest majority on-board are there because they want to be and to be entertained by the Disney experience). True one cannot be oblivious to risk but (again IMHO) someone sheltering a child throughout their young years to too old an age is not equipping them with the tools needed in how to be safe on their own or developing in the child the confidence to learn such themselves.