Perhaps the death of Tzaddikim still involves a problem for Kohanim, or perhaps the Arizal was unwilling to take for granted that he was a Tzaddik? (Note that despite this potential explanation of humility, the Holy Arizal did give his followers specific instructions on the preparation of his body for burial, including the fact that his body would immerse itself in the mikvah and they were not permitted to immerse it for him. So, it doesn't appear that it was an issue of modesty.)
Update: I had the priviledge of asking Rav Yisrael Avihai (Rosh Yeshivat Hamekubalim in the old city of Yerushalayim) about the Arizal's position of kohanim visiting the graves of Tzaddikim. He said it was forebidden.