Dueling dishes, and/or splitting the difference

Our son had the rather interesting idea that, since we're almost always milshig/chalavi/dairy for breakfast and lunch, we should keep the sink milshig and the dishwasher fleischig/b'asari/meat&poultry, so as to minimize the number of kitchen items that end up getting washed over the bathroom sink.  This won't work when we're cooking from scratch, e.g., making chicken soup, and really can't avoid using the kitchen sink.  But we're experimenting to see how well this will work at other times.  Stay tuned.