Negotiating schedules is simply another control ploy. The spouse who cannot relax will not do so just because they have free time. They don’t know how and everything that they do is tied to their self-perception about how other people see them.
The charges handled by the spouse on will never be done the way that they should be and the cycle will roll back to it’s original state.
Sorry to be a pessimist but after 3 decades, taking over the cooking 5 nights a weeks, hiring a house cleaner plus sharing any other chores, my wife still finds new way to exhaust herself.