Or how about the candidate who lands in second place becomes vice president? LOL. Imagine what the present presidency would be like with Hillary in the West Wing.
We’ve had it both ways in the US. In the beginning, the runner up became VP. Then, in 1804, the president and vice president were elected on separate ballots as specified in the Twelfth Amendment which was adopted in that year. As more and more states began to choose their electors by popular election instead of appointment, candidates began to realize they could run together as a team for president and vice president instead of running separately for each office.
The practice of a presidential candidate having a running mate was solidified during the American Civil War. In 1864, in the interest of fostering national unity, Abraham Lincoln from the Republican Party (popular predominately in the North) and Andrew Johnson of the Democratic Party (popular predominately in the South), were co-endorsed and run together for President and Vice-President as candidates of the National Union Party.
The National Union Party disbanded after the war ended, with the result that Republican Lincoln was succeeded by Democrat Johnson; the states began to place candidates for President and Vice-President together on the same ballot ticket, making it impossible to vote for a presidential candidate from one party and a vice-presidential candidate from another party, as had previously been possible.
If we dispense with the electoral college, we could go back to voting for both positions separately and that is one of the reasons both parties resist it.