^All of this was fulfilled in the time of the Apostles. There's nothing to indicate this special charge extended beyond the life of Peter or applied to some group of Romans thousands of years later.
As to female clergy, there is a very curious reference to a female Apostle Percilla.
I see the nature of the gender roles as having similarities to the modern parlaimentary system. The man is to be Chief of State(household) and the women should serve as Head of Government(household.) The Father should be given honor as The Chief but we all know where the real power over the family matters resides in a healthy system.