The Democrats and Republicans think that they can just do whatever they want. Both parties should be ousted and politicians who will actually represent the people should be elected. As stated by minnie1, an independent does not have to believe in any one way or another just because he/she is a member of any one party, and can better choose what is best for the American people, based on what the people say. Also, more competition would probably help fight corruption, as politicians who do not represent the people would not be reelected as easily.
The only third-party candidate winner would need to be an Independent. We need someone who's not for or against either party of the Democrat or the Republican to bring bi-partisan and continual compromising into our government. People who are independent are more adaptable to controversial situations and are better negotiators. The third party candidates are most generally in the election for the people and the good of this country and don't put themselves or party name first.
The only way it would help the state of American politics would be enough independents got elected to make sure neither party's had a majority in congress. Otherwise, they would just be unnecessary votes. Additionally, many third party candidates are even more partisan than the republicans or democrats (looking at you Bernie Sanders). These politicians would just proliferate partisan deadlock and waste Congress's time by proposing legislation that has no chance of being passed.