It is not true that “every other country” has parties select their presidential (or nearest equivalent, whether as head of state or head of government, other countries frequently divorcing those roles) candidate by simultaneous national elections. Sometimes, they don’t even (in a legal sense) choose a candidate at all, though the party may have its own process of deciding and announcing who its members responsible for the leadership election (e.g., MPs in Westminster-style system) will vote for should they secure the necessary majority to decide the outcome on their own.
In fact, I couldn’t off the top of my head name even a single country that uses a national simultaneous primary to select party nominees for election head of government or head of state, can you?