Well historicaly AEA (actualy existing anarchism) that opperated at non insignificant scales for non insignificant timespans (Makhnovia, Catalonia) one way or the other didnt have freedom of press for non anarchist or non anarchist leaning publications and groups

when it is made, it would reflect the diversity of ideas and driving ideology of anarchism, would it not

Not exclusively unless you've completely eradicated all internal and external reaction and the forces of imperialism.

You would be flooded with counterrevolutionary propaganda and have no acceptable means of getting rid of it.