Admittedly, policymakers, once they recognize their mistake, would presumably want the economy to run hotter for a time to restore the previous rate of inflation and would thereby make up for the initial output losses. But coming to the realization that the original assessment was mistaken and that asset prices were in line with fundamentals is likely to take some time.
And the mistaken call would have reduced welfare by needlessly inducing fluctuations in the macroeconomy. Timing is also an issue. Let us suppose that the evidence is so compelling that policymakers become fairly confident that valuations are excessively rich.