You would have a lot of murders and impeachments.
Since most would vote for the opposite party to balance things, and the party which loses the presidency would try to remove the President for it's Vice President to take over.
I think people would still vote straight ticket in this regard. Especially nowadays. I think one exception would honestly be 2016, where enough third-party Never-trumpers may sit out the Pres vote but vote for Tim Kaine and allow him to barely defeat Pence.
I think both Biden and Harris would defeat Trump and Pence. Yall forget how badly Pence did in his debate with Harris. Plus he's a total dud of a candidate period.