The constitution requires that national government to “guarantee to every state in this union a republican form of government,” but the supreme court has refused to define the term “republican form of government.” why is this the case

The Supreme Court has refused to define the term “Republican Form of Government" because it has not a idea of how to interpret the right meaning of that statement, but often in the schools is taught that the right meaning of that clause is that the National Government guarantees that representative democracy is implemented in all states of the Union and not the direct democracy, but that is a wrong interpretation of it's meaning, because never was prohibited the direct exercise of democracy. So, Which is the right meaning of that term?, well the right meaning is that the term "guarantee to every state in this Union a Republican Form of Government" means that the National Government forbids states to change their state constitution to implement monarchy or aristocracy forms of government, because in 1789 after the confederaton articles were approved and due to the inestability of the new nation, the fear of that some states decided to go back to a monarchy or aristocracy was common, whereby the National Government with the approval of the clause said before, forbided the monarchies or independent aristocracies in the states, to avoid damaging the nation.