Major political parties do not use First Past The Post when electing a new leader. Not even the BC Liberals who are fighting to keep this antiquated voting system.
You would want to make sure that the leader of your party had the support of the majority of the party members. You wouldn’t just say “Phil got 38 per cent of the vote but since that’s more than anybody else Phil’s our new leader. All hail king Phil.” That would be a stupid way to run a party.
It’s also a stupid way to run an election. But that didn’t stop Quebec from using First Past The Post during their last election with four parties running. Philippe Couillard won a majority government with only 38 per cent of the popular vote.
He now has absolute power over a province where 62 per cent of the people didn’t want him to be Premier. Good luck Quebec. Maybe next time try Proportional Representation.