It was a mixed bag for our four year old. He did request to go and was always happy to be dropped off for a while, but it is certainly not an all day thing at that age--we usually got the call to get him about an hour in, which was fine with us since I love my family time. We found it was important to arrive just at the time an activity he wanted was starting because that way we could make sure he was in the right section (club or lab) and didn't miss it, because participation in activities is self-directed. Overall, he did enjoy it, especially the character activities.
That said, I am in the camp that it is very chaotic, at least on the large ships (maybe this is better on the classics where there are fewer kids total). We did get called to pick up various kids on several occasions because they had been injured by other kids running or hitting/kicking, but I think that is just to be expected any time you get a large group playing together (think recess at the school playground). The time of day definitely makes a big difference, since it was always craziest in the evenings and least crowded in the mornings.