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Here: My guess is that it has to do with the poet's own attempts at playing historian for his own Athens.

A person like a historian is of course a countable entity, but in this case though HISTORIAN stands alone, I feel it's correctly used, but I just couldn't think of a good reason; could you tell me why we don't have to add A/THE before HISTORIAN nor an S after it?

Yes, after 'play', as also after 'elect', an undetermined countable noun can be used.

The common factor is essentially the notion of assuming a certain role or identity via, or as a result of, the action of the verb.