I don’t see how closed primaries prevent anyone but those who don’t understand the system from voting. I have been a registered Republican and a registered Democrat. It all depended on who had the more interesting races. Truth is I’ve mostly been registered as a Democrat since they tend to have the more interesting races, if not candidates. 
Not from what I’ve seen.
From my POV, neither of the parties runs toward the center. And both try very hard to court the far left and the far right and it shows in the party platforms and the candidates.
Is there a state where open ballots have had that effect?