Each state was free to set up its internal system as it liked. I don't know for a fact if each state's supreme court is by appointment as opposed to election, if it is for life as opposed to term, and if it has any power to tell that state's legislative branch what to do (and if it does, what power it has to enforce those demands).
But, frankly, I don't care for two reasons. First, what the states are free to do is bounded by the federal Constitution. Thus, on major civil rights issues, only the rulings of the Federal SC matter. Second, since state's SC were not the topic under discussion, then this is a red herring, suitable for pursuit by fox hounds but not by rational people.