Honestly 14 people all getting up and each individually taking their plates into the kitchen is the most obnoxious thing I can think of after a meal. Crowded, messy, potential for breakage, etc. Wow. I wouldn't want to get involved in that either - not because I'm lazy, but because I'm reasonable and intelligent and polite! The letter writer seems to be basing her whole opinion of this young woman on this one thing. No mention of how compassionate she is, or how financially successful, or how intelligent, or whether she's a good conversationalist, nothing. Just "she doesn't clear the table at my home along with over a dozen other people crowding the kitchen!" She doesn't even allow for the idea that maybe such a huge family gathering was intimidating or overwhelming for the young woman.
(PS your link doesn't work, one needs a subscription to the Chicago Tribune to read Ask Amy, I had to google and read it on the Denver Post site)