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I disagree that this is a very small subset of problems, the majority of real life problems let you decide to wait and collect more information or decide how many resources you're willing to bet. See examples in https://en.wikipedia.org/wiki/Multi-armed_bandit
For example, I think I first noticed this problem many years ago in one of Scott's linkdumps where he disapprovingly linked to Obama saying that CIA told him that such and such thing had a 70% probability but really they had no good information so it was a coinflip. And Scott was indignant, 70% is 70% what more do you need to know before you authorize some military operation, even the President doesn't understand probability smdh. In my opinion Obama was right, if technically imprecise, while Scott was wrong, which demonstrates the danger of having a little knowledge and also the need for more awareness.
You say this as if it's not Bayesians' fault that they have not developed (or got into a habit of using) a succinct way of conveying how much of the estimate comes from the prior and how much from the previous updates. I would understand if it was an acknowledged hard problem in need of community's attention, but for example Yudkowsky sequences don't mention it at all.
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