Hahaha! That's funny and true.
*Cough..Cough*
Apparently Skynet didn't have enough information about Sarah because 'a lot of stuff got lost in the war', it only knew the city she lived in as of 1984. It had to rely on the T-800s detective work to find and kill any Sarah Connor it could and hope one of them was the Sarah Connor. So killing her as a child wasn't an option or probably anyone else further back on the family tree.