This crusade was started by pope Innocent III and the king of France. French aristocrats from the north were told that they would have lands in the south if they participated in this holy war. Pope Innocent III started a crusade against other Christians!
Right. The Christian overlords of the county of Toulouse that is. They had done squat about the Catharism per se (other complaints were over how towns were electing Jews for public office, and how the local lords hired base and non-noble professional mercenaries for their military needs). A further accusation was that the knight who had ridden down and speared the Papal emissary at the ford across the Rhône by the major pilgrimage center of St. Gilles after negotiations had again broken down between the papacy and the count of Toulouse had carried out the count's orders. (No one really knows. The most probable culprit was apparently a knight part of the comtal household though. It might be possible he was trying to fulfill what he thought was his lord's wishes on his own initiative or something.)
Point being that the crusade was a call to remove the temporal lords who in the eyes of the church had failed. The promise of land was not just compensation but a move to provide these lands with new, more religiously fervent, rulers. Something the king of France protested against, as something the Pope had no authority to decide. Add to this that the king of France actually point-blank refused to get involved. Some of his nobles went ahead on their own initiative, but the king himself made no move until the royal crusade of 1226, which was a rather different endeavour than the original crusade called by the Pope. And of course there had to be a new crusade because the southerners (Christians and Cathars) actually defeated the first Papal crusade, and sent it packing. (Even if it was only after some very long and hard fighting.)
The death toll in cathars is hard to gauge, but apart from some specific sieges early in the crusade, they weren't targeted nearly much as the temporal lords. After the first summer of crusading the military action for years mostly seems to have consisted of the new counts of Carcassonne (later also Toulouse), the Montforts, setting out to reduce a slew of castles whose lords had sworn him allegiance at sword-point, and then rebelled at first opportunity. They weren't Cathar either. The future saint Dominic was walking through the lands and pretty much concluding that crusade or no, the Cathars were mostly fine (he counted the number of weaving houses they operated in the towns), meaning his new mendicant order based in Prouilles had its work cut out for itself, trying to beat the Cathar Perfecti at their own game of exemplary, selfless and self-denying, life-styles. Success in that was what landed the Domenicans the job of forming the first inquisition, which was somewhat different from the imagery conjured up by the later Spanish inquisition.
After all, there were Cathars in southern France long after the crusades. And the real hotbed of Catharism was the North Italian city-states of the Lombard league anyway. Though of course, there the temporal rulers were allies of the Papacy, in rebellion against their overlord, the Emperor, which meant in order to deal with the heretics there the church proceeded with the more soft-touch options to gradually root it out. Afaik they did so with the compliance of the temporal lords though. Again this unlike what happened in southern France or to be precise the lands of the counts of Toulouse and his vassals (meaning the Imperial lands east of the Rhône were safe, as were the lands of the king of England to the west, and various major towns like Aragonese Montpellier or Papal Narbonne.)