Third parties thrive in parliamentary systems but in the United States they are usually important only if they change the plurality in a swing state in the general presidential election. Any third party can frustrate the will of the majority of the people by slicing off a few percent of the votes as Ralph Nader clearly did in Florida in 2000, thereby giving the presidency to George W. Bush.
I was friendly with the future president in college and I can testify that he never expected Nader to make him president.
I was part of a group that tried to persuade Nader to drop out in 2000. He knew exactly what he was doing. He wanted to help Bush win in order to prove that there was no difference between the two parties. The logic was lost on me.
But as Nader proved, the existing presidential selection system gives great negative power to an American third party. I fully expect that dark money at some point will fabricate third parties out of whole cloth with the specific purpose of repeating the story of Florida 2000 in the half dozen swing states that matter under the current system.
This tactic might be tried in 2020.