The danger is that they then announce these numbers as if they have any real-world basis, and that they are taken as making a claim about objective reality.

There's no evidence I know that pulling a number out of your backside and running it through Bayes' theorem produces better results than just pulling the number out directly and running with it. Indeed, the real-world track record of LessWrong/MIRI (to bring this back to topical relevance) strongly suggests it's less effective.