Poets and teachers and such are the most visible and obvious targets for a despot. This does not necessarily equate to their being dangerous (though they may flatter themselves that they are) to his rule but he does not care — he dislikes criticism.
Moreover, the populace who put him into power will applaud the destruction of these ‘others,’ these men and women who do not think as they do. There is nothing to be lost — in the despot’s eyes — in making as example of them.
(This is the sort of note I frequently make to myself, to be plugged into a novel down the line. There is a lot of politics in my books!)