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orthonormal comments on Bayes' rule =/= Bayesian inference - Less Wrong
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I can understand how you'd get that confusion from the names of the approaches, but you've got it rather wrong. Bayesians incorporate all evidence that frequentists use, including observed frequencies in large data sets; this results in their posterior distributions being centered very narrowly on the frequentists' point estimate.
In large data sets the Bayesian method gets a similar answer, but it's not the same method. If you flip a coin once, and get heads, the frequentist method would say that the coin always lands on heads. The Bayesian method would never result in saying the coin always lands on heads unless it was assumed from the beginning.
I didn't expect I'd end up saying this, but frequentists aren't that naive either.
What does a frequentist do in this situation?
They won't use that method when it gives results that absurd, but that's still what the method says they should do.