Against Publicly Funded Party Primaries: Why should the people have to subsidize the primary elections of fringe groups like the Democrats and Republicans?

A few years ago, Washington state instituted a "top two" style primary system like that recently adopted in California.  From a letter to the editor of The Olympian in Washington state:

I am increasingly disgusted by the continuing efforts of the Democratic and Republican parties to overturn the "Top 2 Primary" system. In fact, they are convincing me that in the next election I should vote for a third-party candidate - anyone but a Democrat or a Republican.

Political parties were mistrusted by America’s Founders, for good reason. Political parties were not established by our Constitution. Why should my tax dollars be spent helping them choose their candidates? If they want to have an election in which only candidates recognized by the respective parties can run under the party label, let them finance their own primaries. Taxpayers have made it plain that they do not want to finance elections for the benefit of the parties. What part of “no” do the parties not understand?