You would think that fixed bleeds would work quite satisfactorily
in hand-cranked street organs (known sometimes as busker organs) or
fairground organs, but most appear to use adjustable bleeds.  This
applies only to keyless organs, of course, as a keyed organ has no
need for a bleed.  As stated by the questioner, the bleed equalises
the pressure after hole in the paper has passed the tracker bar hole,
and the note can then cease to play.

The bleed hole size is critical in ensuring that the note starts and
stops at the correct time, and that correct repetition is obtained.
This is a function of the tracker bar hole size and the volume change
of the pouch between 'relaxed' and 'energised'.

Almost all player pianos use fixed bleeds, so why does the organ
builder use adjustable bleeds when it must be more expensive to do so?
There must be a reason.

I believe that the reason is due to the design of primary pneumatic
used in organs.  As they work on a pressure system they cannot employ
the pouch but instead use what is called the 'pill box'.  The player
piano pouch operates its valve by pushing, but in the organ, being
under pressure, the pouch would have to pull the valve.

Although possible, mechanically, this design is troublesome to make
and operate reliably so the pill box is used instead.  This comprises
a pair of circular wooden discs connected by a leather cylinder.  One
of the discs is glued to the chest and connected via its central hole
to the tracker bar, and the other disc is leather faced and acts as
one face of the valve.  It is a simple matter to fit a valve stem to
the centre of this disc.  The effective membrane is therefore the
entire curved surface of this leather cylinder.  This has a much larger
area than a circular pouch.

I suggest that the adjustable bleed is required to compensate for
variability in the porosity of the large leather membrane, and other
manufacturing tolerances.

Nicholas Simons, GB