I've been with my husband nearly 47 years.  Neither of us wanted or needed someone to take a "head of household" role.  In some areas I took the lead, in others he did.  It was based on who was stronger in that specific matter - we respected each other's abilities and judgment.
Never would I, my daughter, DILs, sisters, friends, or anyone in my life, defer to a man simply because he was born male.  Nor would my husband, sons, or others in my life expect or want that.
p.s.  Neither of us ever broke our vows.