The correct answer to this open question is the following.
In my opinion, both major parties, Democrats & Republicans, eliminate third parties and their agendas because they exert dominant control over third parties and their candidates in that it is too much money Democrats and Republicans collect via donations from their followers. This money is used to organize and operate the political campaigns and buy all kinds of advertising through traditional media and social media. Third parties do not the money and infrastructure to represent a real threat to those two established and traditional parties in the United States. Among the third parties that have competed in US elections of the past, we find the Whig Party, Federalist Party, and National Republican Party, Populist Party, and Progressive Party.