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Well, it lets you gain Plagued by a Popular Song if you're an endgame character.
That counts for something, because previously the fastest way to get from 230 Shadowy to a level where you could fail any Mahogany Hall checks was <a href="/wiki/Let_their_error_be_eaten" title="Let their error be eaten">Let their error be eaten</a>, which requires 1) Hallowmas, 2) very specific and advanced point in the SMEN storyline.
A non-seasonal, non-SMEN but deck-dependent alternative was to own the Eyeless Skull. You'd need to pull a mere 70 Forgotten Glamours or Forgotten Sleights to get from 230 to 180 Shadowy or Persuasive, then use a Talkative Rattus Faber to get down to 155 (where the chances of failing MH checks are 5% or higher).
If you ask me, a Weasel of Woe is an excellent investment. At a mere 400 echoes, it saves you thousands of echoes' worth of actions.