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VAuroch comments on A Fervent Defense of Frequentist Statistics - Less Wrong
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Well, I'm not familiar enough with Solomoff induction to check your assertion that the frequentist induction is better, but your second question is easy. The average case would clearly be calculating an expected Regret rather than a bound. The proof is accurate, but it's measuring a slightly-wrong thing.
EDIT: Looking at the Blum paper, Blum even acknowledges the motivation for EY's objection as a space for future work. (Conclusion 5.2.)
Expectation with respect to what distribution?
The distribution of the 'expert adivsors' or whatever they actually are, their accuracy, and the actual events being predicted. I recognize this is difficult to compute (maybe Solomonoff hard), and bounding the error is a good, very-computable proxy. But it's just a proxy; we care about the expected result, not the result assuming that the universe hates us and wants us to suffer.
If we had a bound for the randomized case, but no bound for the deterministic one, that would be different. But we have bounds for both, and they're within a small constant multiple of each other. We're not opening ourselves up to small-probability large risk, so we just want the best expectation of value. And that's going to be the deterministic version, not the randomized one.