Open primaries should lead to more voter participation with more candidates in the democratic process. Even better, places like California have the top-two winners of primaries moving on to the general election, regardless of party affiliation. That way, the favorite candidates move on to the general election a few months later. The only downside is that members of both parties could try to sabotage certain candidates by voting for another. Aside from that, more voter participation is always welcome in the democratic process.
Open Primaries are an improvement over closed primaries, but top two nonpartisan primaries are best because everyone gets to vote in the first round for the same candidates. The parties are not given special privilege. Giving parties control over a process paid for by the taxpayers, is detrimental to democracy. 40% of the country identify as independents and are excluded simply because they don't support partisanship.