I figured it eliminates additional material for the NaOH to break down and increases the possibility of cleaner solvent pulls.
If you're doing the extract quickly over the weekend or whatever, maybe it's not as necessary. But if you're leaving the basified soup on the side for a little while because you haven't had time to do that last pull or whatever, fridge decanting and filtering out bark particles certainly won't hurt.
Also it give the acidic soup a much nicer shade of transparent red