I found this unattributed quote which offers some raison d'être for the enterprise of writing - even when nobody other than oneself will ever get to read one's words:
'Writing is a means of clarifying to oneself one's own ideas.'
To this one can add something from another note that I found stashed away, that the point or use of poetry is to explore ideas that cannot be expressed in any other way. Different forms of language not only allow different forms of expression, they delimit and confine as well. Different types of ideas need these different forms of expression in order to be fully realised.
The two separate ideas above combine in the writing of poetry. Poetry is popular but perhaps not popular enough. There is perhaps not enough poetry in daily life; one does not encounter it by accident often enough. If one did, perhaps we might be a more thoughtful and richer society.