We just got back from Italy as well and thing you have to remember is these are guided tours with close to 40 people. Even if your children travel well, there are many situations where meals last one to two hours and there just isn't the opportunity to leave if your child is tired or bored. In addition, as the other posters stated, Italy is not at all stroller friendly. A child would really have to be able to do the walking on their own.
When you are with the group it is great because you get to know everyone and all the travel details are taken care of. On the other hand, if you are in a museum your child thinks is boring, a long meal, or the end of a long walking tour, you just can't opt out. It is a different kind of experience than traveling as a family and having more flexibility. I do not think my kids could have enjoyed the experience much younger than 10 and they are great travelers, but they are used to vacations centered around them. In others words, you usually go to restaurants your kids like, attractions your kids like, and stop and get them treats and snacks when and where you want. We you are with a group you go on their schedule and you just can't get a soda whenever you are hot or even go to the bathroom whenever you want. Although, the kids on our trip were great you could tell that they were really tired and bored alot. Our guide told us the trips were all designed for children nine and over and that most of the time the younger children are just along because they have older siblings.