Replace "adversarial superintelligence" with "adversarial game", and I think you'll get more agreement among the participants. There are plenty of cases where a "mixed strategy" is optimal. Note that this is not noise, and true randomness isn't necessary - it only needs to be unpredictable by the opponent, not necessarily random.

Where you don't have an opponent (or at least one that makes predictions), I'm with Eliezer: noise never helps at a fundamental level.

I do believe that randomness has a place in thinking about problems, and it's easier (for humans) to reason about randomness than insanely-complex deterministic calculations. But that's a problem with the reader of the map, not with the map nor the territory.