The President and the Vice-President are members of the same Administration - they are expected to co-operate in getting the President's agenda through Congress. If the Vice-President is critical or unsupportive of the President's agenda, it makes it much more difficult for the Administration to achieve its goals. Also - if the President is ever sick or incapacitated for some reason, the Vice-President would be Acting President. To have a person take over who disagreed with the President's decisions would cause confusion and difficulty.
Back when this was still how elections worked, a common problem was that the President would be from one political party while the VP was from another.
A political concept is a system devised to deal with the "Friend-Enemy" complex on a political level. Without "enemies" there would be no need for politics.
The two leaders might be political enemies
For one, the Iceland nation relies heavily on whaling. So the political enemies would be whaling. Other enemies may be countries such as Afghanistan that oppose such movements as the NATO.
The election of 1796 had to be decided in the House of Representatives. John Adams had the most votes and Thomas Jefferson had the second highest votes. So Jefferson became vice president. The problem is that each was from a different political party. So there was a call for the 12th amendment to have electors decide who would be president and who would be vice president on the ticket.
They had no effect on the election of a president but had complete control of who would be vice-president.
Every office-holder, especially the President, has enemies, but we would certainly hope those enemies would not want to kill him, since doing such a horrible thing solves nothing and is really bad for America as a country.
That depends on your political party. A Republican would believe that a Republican president is best, while a Democrat would believe that a Democratic president is best.
Political parties.
As president, Nixon would have officially considered the following as "enemies" of the U.S. : North Viet Nam, North Korea, Cuba, the USSR and all Eastern Block nations. Not to be confused with Nixon's famous "enemies list" that refers to people and organizations in the U.S. that he personally considered his political enemies.....such as prominent Democrats, members of the media that maligned him, as well as some prominent judges, and senior FBI executives who had worked under J. Edgar Hoover.
The goal of the opposing party is make the president look bad and defeat him in the next election. The vice-president presides over the US Senate and can cast the deciding vote in the case of a tie. It would undermine the administration to have a vice-president working against it.
There is no such Ammendment and would almost never happen in today's politics as you would want someone to be on the "same page" if you were unable to fulfill the duties as president