I think this series of posts should contain a disclaimer at some point stating the usability of randomized algorithms in practice (even excluding situations like distributed computing and cryptography). In a broad sense, though randomness offers us no advantage information theoretically (this is what you seem to be saying), randomness does offer a lot of advantages computationally. This fact is not at odds with what you are saying, but deserves to be stated more explicitly.

There are many algorithmic tasks which become feasible via randomized algorithms, for which no feasible deterministic alternatives are known - until recently primality testing was one such problem (even now, the deterministic primality test is unusable in practice). Another crucial advantage of randomized algorithms is that in many cases it is much easier to come up with a randomized algorithm and later, if needed, derandomize the algorithm. Randomized algorithms are extremely useful in tackling algorithmic problems and I think any AI that has to design algorithms would have to be able to reason in this paradigm (cf. Randomized algorithms, Motwani and Raghavan or Probability and Computing, Mitzenmacher and Upfal).