Why doesn’t ‘democracy’ have the second place finisher becoming the vice-president? That would shake things up.
That actually was the original system, but the development of formal political parties mucked it up. Electors voted for two candidates, and any candidate receiving the highest electoral vote total became President and the second place finisher became VP.
The problem with this system became apparent in the election of 1800. This was the first election in which there were formal political parties. Naturally, each party had two candidates. The Democratic-Republicans defeated the Federalists, but their electors cast equal numbers of votes for both Thomas Jefferson and Aaron Burr. That threw the election to the House of Representatives. The House had difficulty reaching a majority because The Federalist-controlled delegations supported Burr in opposition to the Dem-Rep party leaders who favored Jefferson (who the party had intended to be their actual Presidential choice all along).
Eventually the Delaware delegation (Actually just a single Representative) ended up supporting Jefferson and breaking the deadlock. The 12th Amendment was ratified before the 1804 election to fix the system, and this put in place the system currently in use (essentially the same - the 20th Amendment made some slight modifications dealing with cases where no EC majority is attained).