We were just on the Divina over MLK weekend and had a similar experience as the OP. While we expected a full ship (we had 4200!), we also expected they would be staffed to serve that many. They weren't. No plates or silverware on the buffet, running out of food, lines a mile long, no place to sit (due to tables not being bussed) if you were able to get food. None of the flavors of gelato needed to make the shakes they advertised. No Diet Coke! How do you run out of Diet Coke?!? We had good service in the dining room and the food was "ok". We also didn't have an assigned dining room or time, but we stood in line before sail away and were given one.
We sailed on the Meraviglia 11/22 and didn't have any of these issues. Of course, the ship was only half full, so that helped. We had a terrible dining room experience on the Meraviglia (over an hour to get our food, the wrong items came out, plus they were raw), so we ate all of our meals on buffet and enjoyed them.
Sounds like MSC is only staffed for half-full cruises.