On a slightly related note, what would happen if each party presented two candidates to be voted for in the general election? In retrospect it seems designed to do little more than offering people (theoretically) Marco Rubio vs Donald Trump vs Hillary Clinton vs Bernie Sanders; it seems like a logical way to avoid extremes being the only option as well as two suboptimal options being the only ones available.
It would also lessen the possibility that a single loud (and unqualified) voice could dominate party primaries where the media covers one spectacle for ratings and ends up diminishing the relevance of other candidates due to the opportunity cost of covering multiple candidates.