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.