Why would Klaus have killed Katherine's family, as wiping out the Petrovas would prevent another dopple ganger being born?

He killed them to get revenge on Katherine for escaping him.

And I assume (although I could be wrong) that a Doppelganger would only be born from a direct decendant of Katherine, and as Klaus was unaware of her daughter he thought his chance of breaking the curse was gone, so he had nothing to lose by slaughtering Katherines family.