People should be allowed to vote for whoever they wish. One would assume that the vast majority of people will vote for who they want to win. The problem I have with the closed primary system is this: the presidential preference primaries are funded by the states. There is a virtual media blackout of any candidate not inside one of the two major parties, with both colluding through mutually agreed upon debate rules to exclude other candidates from the conversation. This makes it nearly impossible for an independent or third party candidate to get the exposure necessary to be competitive. So long as these party primaries are funded with tax dollars and our system remains heavily slanted towards electing only Republicans or Democrats, independent voters must be allowed to participate. No taxation without representation!
The current Democratic race is proof that open primaries lead to vastly different electoral outcomes, more in line with what the majority of Americans want.