You are going to see responses both ways similarly whether it is MSC YC or NCL Haven. For YC, as pointed out, there really isn't anything geared towards kids other than food (not kid type food necessarily, just an abundance and variety).
We've done three - the first was Divinia during the summer time. There was an extended family there with one of the families consisting of Octomom. Whenever we ran into them, they were all over the place doing things that should have been corrected by parents. They even let the diapered kid into the YC pool. Even outside the YC, the dads were trying to track down the kids who had gone several floors up the stairs and kept going. We spent a lot of time in YC areas and luckily this family wasn't too much which made it tolerable.
Second trip was during March and there weren't many kids surprisingly during spring break time. Third time was again during the summer and there were quite a few kids, even younger. All were well behaved. Many were always out by the pool just chilling in the loungers or pool (note their pools are pretty deep in YC). The TSL really doesn't seem to appeal to them much when there is so much else around the ship. We only saw one instance where three kids were running around in the TSL while parents were there.
Both MSC and NCL in some ways promote these areas for families so ignore any cranks who say no kids should be allowed since both lines allow it. Obviously though, it is on the parents to be parents which as you go about doing things where you live, you see that not always happening.
Bottom line, you'll probably spend quite a bit of time outside of the YC but the YC does offer (normally) a very quiet and less crowded area with great services.