What messes up my analysis of this issue is that the clerk has an elected position. She isn't just a hired administrator. Since the legislative district has chosen to place an elected official in the post, that seems to grant additional options to the official. That is, if the voters decide that they want a clerk who does not issue licenses, even though that seems to be a disservice, they are getting what they voted for.
If those voters then decide that they don't want the clerk, then there should be an official process to remove her from office.