"And then what you're saying is that the Universal Prior only applies to SIHs, and not (at least, not directly) to hypotheses such as "this patient has cancer".

I agree that Solomonoff induction isn't particularly relevant to most practical cases. Solomonoff Induction tries to explain what your prior should be if you didn't know anything about the world. But in any real context, we actually know a lot about the world.

Medical diagnostics is an apt example. Here, we have especially good priors, since we have accurate medical statistics. We can measure the overall incidence rates of cancer in the population overall, and typically we also have statistics for particular age and sex cohorts. There's no reason to start from "how easy is it to write a program to describe 'cancer' in some fixed language."