There is no correlation between the openness of primaries and the relative influence of parties in states. There are open primary states with strong parties and closed primary states with relatively weak parties. In fact, in several states one or both major parties have petitioned the state to open their primaries to unenrolled voters.
"We believe that one of the most important things we can do to strengthen our party and our democracy is to invite independents, especially young voters, to participate in primaries." - Jane Kleeb, Chair, Nebraska Democratic Party