Here is a description of the court hearing held August 3 in Phoenix, over whether the initiative for a top-two open primary should be on the ballot. Opponents argued that it violates the single-subject rule. The only argument on the single-subject rule that seemed to give the judge pause is the point that the initiative unnecessarily abolishes elections for party office. The very last paragraph of the article mentions this.
The other states with top-two open primaries, Washington, California, and Louisiana, all continue to hold elections for party office.