My children have been eating at fine dining restaurants (on land but also on Princess, Regent, and Celebrity) since they were a few years old. They are much better behaved than many of the older passengers we encounter in specialty restaurants. When they were younger than 5, they would occasionally get antsy and one of us would remove them from the restaurant to go for a walk or to bed early, but that has not happened since they were school aged. FWIW, the discount cover charge for children has been in place for many years across most of the lines we sail on, including Princess and Celebrity.
If I could count all the annoying individuals I've witnessed in dining rooms, less than 1% of them would be children (and more than 90% of them would be large groups of drunk people). I know that there are irresponsible parents and bratty children that give everyone a bad name...many cruisers come and remark how delightful and well behaved our kids are. I also would be annoyed if loud and unruly children were seated near us (whether in specialty dining or the MDR), but I don't think you should assume that children aren't capable of behaving just as well as the median adult.