I'm going to approach this from the other side, as one who's done this. Not that the above reasons aren't valid... a lot still depends on the itinerary, ship, parents and kids.
Our son's first cruise was at 11 months, and his second at 20 months. We were fortunate in that both cruises left from nearby ports (no long flying or driving days), and were not port-intensive (we went to Bermuda). That worked out very well as we didn't have to be concerned about car seats in Bermuda, as the places we went were all walkable and stroller-friendly. We made sure to request a table for just our family so that others would not have to put up with the eating habits of a 1-year-old. We sat in the back of the show lounge during shows to make a quick escape, if needed.
The ship is actually the easy part. Sure... you'll still have to take care of the kids 24/7 (unless you opt for the late night babysitting in Camp Carnival), yet many of your daily chores will be taken care of for you. No cooking, no major cleaning, no deciding where to spend a day. My husband and I took turns with our son to give the other a break. Come to think of it, we still do 16 years later.
On the down side, kids who are not toilet trained are not allowed in the pools... health reasons. I don't recall Carnival Victory having a splash area for kids, but I could be wrong as I wasn't looking for it.
Also, the itinerary, as Cas mentioned, may be tough. My main concern was the safety of traveling in local vehicles. Even if you lugged two carseats along, there might not be seat belts to secure them. Plus, port after port can be tiring even for adults.
So, for all of those reasons, I wouldn't rule out taking a cruise with kids who are nearly two years old, although I'd look at other options for ship and itinerary. Cruising with young kids can definitely be a vacation, it just takes some initial legwork to determine the one(s) that are right for your family.