How well does running as an independent work in the USA, historically?
It doesn't do very well.
Currently there are only two who were elected as Independents: Bernie Sanders and Angus King in the Senate and both caucus with the Dems. No one elected as Independent currently in the House. Most of the time someone will be elected either as a Dem or GOP and then switch to Independent. There are none of that ilk in either the Senate or the House at the present time.
Having 3rd party candidates does divide votes and can definitely affect the outcome of an election. In fact, some experts posit that Jill Stein cost Hilary Clinton the election in 2016 by affecting the votes in Michigan, Pennsylvania and Wisconsin (swing states). Had those voters voted for Hilary, she would have won the popular vote AND had enough votes in the electoral college. But that is an 'if'. The Stein voters may very well have stayed home.
FWIW my very inexpert opinion is that post-Trump, and especially if MAGA collapses, we will see more Independents winning elections. I don't think the Presidency, but Congressional seats and local and state offices. People are disaffected with both parties and are looking for alternatives.