the parliamentary systems of the UK ... have the parliament elect the Prime Minister and likewise don't elect their leaders by popular vote. This isn't totally

the parliamentary systems of the UK ... have the parliament elect the Prime Minister and likewise don't elect their leaders by popular vote. This isn't totally accurate: the leader of the winning party is basically the Prime Minister. You vote for the party & leader together, you can't have one and not the other. The system is otherwise just as broken as the US; meaning that outcomes are decided by a small number of "rural" people combined with gerrymandering.