The submission of wives was already well known in the ancient world. Which would suit most married women just fine. Similarly the submission of children and slaves had been taken for granted. Paul's analogy of a local church as a body with many kinds of function is in any case incompatible with a patriarchal wielding of authority. It requires a mutual submission of members with many different gifts, of whatever sex or age or class, to one another.
Listeners submit to whoever is teaching or giving a prophecy.
Pastors submit to the flock. Those with gifts of healing attend to the sick. All are to serve and love all others in the family. And the mutual submissions of husbands and wives to one another is one part of this surprising new kind of organism. We might compare headship and functional differences in any sport.