Virtually all Gohonzons are reproduced by some method of mechanical printing.
I understand the question your asking is actually why not just reproduce a Nichiren authored Gohonzon, instead of that of a cleric or some authority from any of the various schools? The reason that this is not done is because of the doctrine of a "person to person transmission" of the Great Dharma, from a master to his successor.
This doctrine stipulates that the head of a school is the recipient of the enlightenment of the original teacher, or master, which in this case is Nichiren. In other words (and I have heard many clerics within Nichiren Shoshu state this) the sitting master acts as an intermediary for all clergy and laity wishing to obtain the same enlightenment as Nichiren. Therefore, one of the first tasks of an incoming new the High Priest is to inscribe a new Gohonzon and that Gohonzon becomes the standard during the tenure of that particular High Priest. It has even been argued, albeit unsuccessfully, that all older Gohonzons should be returned to the Temple in exchange for a new one at each changing of the High priest.
Nichirenista, the question is a contentious one as it throws fuel on the fire of the schism that exist between the different schools claiming orthodoxy. My own view on this is that orthodoxy is a fundamental obstacle for everyone as it has no recognizable solution. If anything good might come out of this, it is that these disputes should encourage us to turn towards Nichiren's oft stated assertion that the Gohonzon can only be found within ourselves and that the responsibility of orthodoxy becomes a personal quest to move towards a greater understanding of the Original Great Dharma, an understanding realized through faith, practice and study