If your loss function is severely skewed, you do NOT want to be unbiased.

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Actions is what you should care about -- if these are determined, your beliefs (which in this case do not pay rent) don't matter much.

So why would I want to bias myself after I've decided to take excessive precautions?

I think we're in agreement btw, we care about actions, and if you have a very skewed loss function then it is rational to spend a lot of effort on improbable scenarios in which you lose heavily, which from the outside looks similar to a person with a less skewed loss function thinking that those scenarios are actually plausible. I was just trying to point out that DanielLC's reply was correct and your previous one is not - even with a skewed loss function this should not produce feedback to the actual beliefs, only to your actions. So no, you DO want to be unbiased, it's just that an unbiased estimate/posterior distribution can still lead to asymmetric behaviour (by which I mean spending an amount of time/effort to prepare for a possible future disproportionate to the actual probability to this future occurring).