I use "randomness" in a sense that doesn't have anything to do with unpredictability. It only relies on observed long-run statistical properties: limiting frequency, stddev, law of large numbers, frequencies of substrings... For example, the binary expansion of pi works fine for my purposes (if pi is a normal number), even though it's perfectly predictable by an algorithm.

Okay, but then you shouldn't say that failing to know the sequence is not a property of his ignorance. If pi works here, then not knowing the next digit is indeed a fact about your ignorance (specifically, ignorance of the result of a known procedure).

Edit: nevermind, I had misread that: yes, it makes sense to that that the agent is ignorant of the result, but that the randomness is not a fact of that agent's ignorance.

My idea is rather that the 3-world and friends are too crazy to support any life at all.

Yes, but that's still part of the anthropic argument for the Born rule, just on the other end of boundary.