It’s possible that it is just delayed graft incompatibility, but I lost several kaki this year to what appears to be SDS, and the fact that they were all afflicted within a short period together with the fact that there was wide variation in the trees affected (from trees just on their second or third leaf to well-established, productive five year-olds) makes me think that a pathogen is probably involved.
It seems that one of the most reasonable views, in light of the evidence, is that kaki SDS is caused by a pathogen that is lethal to D. kaki but to which D. virginiana is immune, and that the immune response of the rootstock is what kills the graft. This is what makes the disease appear to be due to rootstock incompatibility, when in fact, that may be just a symptom.
You can read about my experience this year, and the opinions of more educated contributors, here: Kaki sudden death syndrome -- help?
I hope it doesn’t hit you. I really enjoyed my kaki persimmons for the same reasons you do. I still have several that are unaffected so far by KSDS, but I’m pessimistic now, because if it is a pathogen, that pathogen is definitely here in my area.