The Romans, and later Empires like having a simple way of treating everyone who is not part of the "correct" part of Christianity as fair game to kill / enslave etc.

Those branches (such as the Cathars) who were more moderate tended to get wiped out by the expansionist xenophobes. So the whole point is to maximise the ability of kingdoms to expand. If every heathen needed individually vetting as to whether they were good people or not it would really slow things down.