"I think it will actually be possible to cure most human disease in ~5-10 years, as crazy as it may sound" is a direct quote from Dario Amodei. In his original essay he makes clear that that doesn't mean all those cures will be distributed to all on that time-scale, but I would still interpret this as a wildly ambitious prediction that AI will cure most diseases. He predicts in the same essay that it will be responsible for a 10X speedup in drug development.