If they are funded, even partially by the state, then the state can dictate how those primaries are run. We have a quasi-open primary here in Cali because that's what the people asked for (the friggin' idiots!)
Caucuses are the cheapest way to run a nomination because you don't have to rent out facilities or hire people to run the polls.
The person who pays the piper gets to pick the tune.
Well, it looks like there isn't going to be any music at this dance.