Good question as well! I should add motivation to the notes on this point.

Basically, we study deterministic mathematical objects within formal systems because these cases are easier for us to analyze and prove theorems about; it's an example of looking first under the streetlight before meandering farther into the darkness. Hopefully this way we'll notice many phenomena that still hold when we add randomness, bounded computations, and other realistic limitations.

And indeed, plenty of the topics in MIRI research do hold up when you make them messier. Many of the topics in formal systems can handle random variables just as easily as deterministic facts. There's a version of Löb's Theorem for bounded-length proof searches, and tracing it through shows that Löbian cooperation and other phenomena behave the same there as in the unbounded case (for sufficiently large choices of the bounds). Using quantum random variables to evaluate logical counterfactuals doesn't solve implementing UDT, it just collapses it into CDT; so we still need to study logical counterfactuals. And so on.

Also, when I say "formal system" you can usually substitute in "Peano Arithmetic" or "Peano Arithmetic plus some extra axioms".