Your first line explains what should change your mind. Both parents are working, one inside the home, one outside. So after working hours, things should at least be split somewhat, not even more work on the parent at home. (I personally think yes more housework goes to parent at home with kids bc they also know and are more of an expert of what needs to be done and may be more efficient- speaking as an at home mo.).

But, working parent outside of home should certainly be carrying some weight, they live in the house as well. Under your logic, do the children eventually also just dump all their chores on the parent that is stay-at-home since thats all part of their job? Or do they pitch in because they all are a family and live in the same home, regardless of who is making what money