At least in Minnesota primaries are unfair to parties.
Minnesota requires major parties to have open precinct caucuses in the spring of Congressional election years. That is, any voter can attend one caucus in their neighborhood (all caucuses are generally held on the same night). Each caucus elects delegates to a district convention or county convention. These conventions then elect delegates to the state convention. Each caucus or convention elects officers to carry on party business until the next caucus or convention.
Many of the people who appear at the caucuses raise money for the party and otherwise volunteer their time to promote the interests of the party. At the higher levels they endorse candidates or select committees to do so.
This bottom-up structure didn't always exist. Parties were often top-down and candidates were selected in "smoke-filled rooms". The primary elections were a "reform" to have candidates determined from the bottom-up.
The downside of this reform was that people who otherwise show no interest in the party, never show up at meetings, and don't give a dime to support the party have the right to vote in the primary. Worse yet, people who support another party have the right to "cross-over" and vote against the primary candidate they think is the stronger, therefore giving their own party's candidate a better chance of winning.
I would rather see a wide-open primary where each party's candidates run against all comers - independents, "third-party" candidates, and dissidents from the major parties. The top two vote-getters then go on to a general election. However, if any candidate gets more than fifty percent of the primary vote, he or she is elected to the office.
There are several upsides to this. People would be more likely to turn out for the primary because they will turn out to vote for their first choice. It would loosen the two-party duopoly, allowing new parties to grow and tired, old parties to lose influence. It would broaden the appeal of voting from the either-or choice of "the lesser of two evils". And the fifty-percent rule would save candidates from campaigning unnecessarily against a candidate "who has no chance of winning."
I also posted this to Harry Welty's blog.