Can't possibly be more ridiculous than what we have now...
What if there were a system where only members of a certain party could vote in that party's primaries, but only independent voters could vote in the general election?
So you want to create the craziest cluster of strategical voting ever?
The number of registered independents would skyrocket as everyone wants to keep their vote and only a small group of diehard ideologues would stay active in party primaries. The result would be general elections between someone like Bernie Sanders or Alan Grayson versus someone like Michelle Bachmann or Herman Cain. Basically, the "lesser of two evils" problem intensified greatly with the disenfranchisement of those remaining in a party, too.
No see my answer... This would lead to some hilarious party switching trying to rig the election.