Is the national party leadership of the Democrats or the GOP allowed to prohibit the statewide party subdivisions (or whatever they're called) to hold caucuses?
If states require parties to hold primaries, the states have to pay for them.
If the national party required the state parties to have a primary, and the state was not funding it, the primary might go badly. The parties might not have up-to-date registration records, they would have to pay wages to all the election workers, and might have to pay market rates for renting polling places and voting equipment.
If the national party required primaries, the state parties would probably force the states to hold primaries. Almost all legislators are Democrats and Republicans, and when it comes to elections they are primarily interested in what is good for their party. They may be more altruistic with regard to other spending.