If the US returned to the law that the 2nd place candidate in the presidential election became VP, would it help current political tensions?

Moot point. since its wont happen. It would only have value if there was more than just 2 major parties.

It was quickly dispensed with because it increased tensions.  1804  after only 4 elections with VP going to second place.

I don't think Biden wants Trump as his V.P. 

I think in today's political climate, that would just mean more assassination attempts on POTUS.

The sore losers bump off the winner and their guy advances to the Whitehouse.

I think you’d see more presidential assassinations. See the Roman Republic. They had a two consul system. Every other day you’d be 😃/😢

Might lead to some violence in the Oval Office. We can afford changing the carpet only every four years.