We cook quite a lot, also with the children and with friends. Except for larger celebrations, the kitchen is actually always cleaned up right afterwards. We've always lived that way; pushing all the mess to the next day is not our thing, and at the same time as cooking, we usually clean up the mess quite quickly again. Our children also learn from the start that they should please put their dishes directly into the dishwasher after eating. If it's clean, then it's your turn to unload it.
For those who first make everything dirty and then like to push the cleaning to the next day, a closed kitchen is certainly advantageous.
I can understand the argument about odors. If that bothers you, closed is better, although an open door doesn't make the odors stay there... that would mean you have to lock yourself in there until you're done cooking (ok, in the past they just pushed the woman into the kitchen )... but as a family, we really enjoy having a common center, and cooking is an important part of our leisure activities.