To say that they shouldn’t, Is to argue that they should not care about their own welfare. Living in a dirty and unkept home is not only dangerous to one’s physical health but damaging to one’s mental health as well. In fact unclean homes are often a first sign that something is not right upstairs (taking the tv show “hoarders” as an example). It is not normal human behavior live in unclean conditions.
However, If the question is talking about within partnerships, It really depends on the situation. The reason why women became largely associated with housework chores is because the men were capable of caring for ALL of the financial burdens of the family and then some. Therefore, It was a nearly even trade off. The man takes care of all of the wives financial issues and she in turn cares for the cooking and cleaning. However in today’s society, Most men cannot afford to be the sole bearers of financial burden in their partnerships anymore, Therefore it is unreasonable to expect women to bear the burden of housework on their own as well when they work just as many hours as men do.
Financially, Yes. But with house chores like cleaning, Cooking etc. I say in the ratio 20% : 80% for men and women respectively. Men mostly need to work if it's indeed in need. They could work if the wife is sick or when she'll not be around for a while. If she's okay and around, They only do it to please her, Make her feel better you know.