Before the 12th amendment, the presidential candidate who got the second most electoral votes became the vice president. This meant they were usually different parties.
It occurred to me that one thing this achieved was always ensuring that there was someone in the room who would be willing to disagree with the president. He couldn’t surround himself with yes-men.
My understanding was that this rule led to some pretty bad “strategic voting” to try to organize securing both presidency and vice presidency, and became a tangled political mess that was improved greatly by having them bundled together on one ticket.
Of course, if you want to talk about strategic voting, infinitely better would be to kill FPTP voting.