The Democratic party isn’t going to act against its own rational self-interest like that, not even if its rump party/parties would have the upper hand in a multi-party system.
Would open primaries not also be against the party's rational interest? Forgive me for overpersonalizing, however I myself am a registered Democrat because 1) I desire to vote in their primary and 2) I want their candidates to have to appeal to me to receive the nomination. If you don't need to be a Democrat to vote in the Democratic primary, then why should I (or any similarly progressive-minded voter in my shoes) register as one to begin with?