A female Pope?

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Pope Joan is believed to have been the first and only female Pope. Prior to Dan Brown's "Da Vinci Code", the very thought that a female could have duped the Catholic Church was enough to start a healthy debate. The fun has been spoilt a little by the many "Da Vinci Code" debates concerning the female bloodline of Jesus (well any bloodline of Jesus!). Fortunately the Pope Joan story went under the radar and is still widely unknown. Though dates and Popes don't add up, the general story is that a highly educated women posed as a man and became so popular she was eventually nominated to become Pope. Unfortunately during her time as the Pope she became pregnant and gave birth during a procession through the streets of Rome. Why doesn't the Catholic church have women Popes ? It is believed a statue of Pope Joan once adorned the Siena Duomo (Cathedral) in Siena , Italy. How hard would it be for the church to erase evidence of Joan's existence ? What impact would a woman Pope have on the Catholic Church and the world? What would have happened if this event happened today? Would the church ever recover?