The anchor baby issue could easily be solved by a new law that any baby born before 8 months have passed since the mother arrived in the country was conceived in another country and therefore belongs to that country. This would work for any baby born after a visitors visa had expired, because there would be a record of when the mother arrived. For the people who enter illegally and are not recorded, then the baby could only be legal if there is some sort of record that the mother conceived in this country—filing for a SS card, or visiting a health clinic and providing the name.
You make a great point. Life begins at conception.