Yes, in the same way we got rid of slavery, we also got rid of female second class status.
In fact, if we really wanted to think about it, we know that one can't fudge about who is the mother, but there can be all kinds of questions about who is actually the father. There aren't too many times when we take maternity tests, but paternity tests are all the rage. :>)
If we went any direction with only one parent, it would make sense to require the mother be the deciding parent.
I think the Founders believed that expressed allegiance to the USA was a matter of both father and mother having that dedication. A child into adulthood can have characteristics tuned to either father or mother. To choose one or the other parent as determinant was quashed by acknowledging that allegiance to the USA was required of both parents and this was to be such at birth of the child for the child to be ‘natural born’. The Constitution recognizes explicitly ‘citizen’ and ‘natural born citizen’.