WarKirby
Arty person
Infirmaries in FF all remove disease, as does Aquae Succellus and the Pool of Tears. No units doesn't mean no way. That being said, there's a case that High Priests should have it, even if lorewise they wouldn't spend much time tending the sick (but neither would OO or AV)
Medicine is a fairly expensive tech, and fairly deep in the tree. Given the tendancy of some AIs to rush AV and spam diseased corpses, as well as the frequency of plagues/withered results from mutation, dungeon exploration, etc. It's all too easy to get your powerful units completely ruined by catching a disease that you can't remove for a looong time.
I think all basic priests should have cure diosease. Or, how about allowing Herbalists to do it instead. Maybe they could only remove diseased, but not plagued and withered.
I'd also suggest giving all suchh promos a chance to wear off in time. maybe 5% chance to wear off per turn. Generally, if you catch a disease of some sort, unless it kill you, you'll recover from it eventually.