In the history of the United States presidential election, it is exceedingly rare that a third party candidate does anything other than split votes from one (sometimes two) main parties, thus essentially ceding the majority of electoral votes to a candidate most opposite their ideology. You can see this in numerous elections. While occasionally a realignment occurs, statistics are not on the side of the candidate running third party. And this is separate from the phenomenon of little known candidates trying to win a major party's primary. Namely, that winning a primary is an entirely different step from winning a general election.
Given that all modern candidates of note for a third party are aware of the above likelihood of their impact as described above, what is the next main motivation for running as a third party candidate?