Why is there no law of physics that contains the Planck volume? The Bekenstein-Hawking entropy of a black hole contains the Planck surface.
Mead's discussion of the gravitational microscope yields the Planck length as the length measurement limit.
Is there any system where the Planck volume plays a role? (The Planck volume is, arguably, the size of the universe after one Planck time; it is also said to be the smallest possible black hole. But these are quite speculative situations.)
Do more concrete examples of physical systems exist, in which the Planck volume arises or plays a role?
Or again:
Is there any equation for a physical law that contains, after simplification, the Planck volume, i.e., the cube of the Planck length?
And more:
Exactly why is there no equation with the Planck volume?
Added:

*

*Is the reason that the ratio between macroscopic volume and Planck volume cannot arise in an equation at all?


*Or is the reason that the ratio between macroscopic volume and Planck volume must disappear (in the limit) for quantum theory and general relativity to make any sense?


*Or is the reason that holography is valid in nature?


*Or is the reason that volume is not built from many smallest volumes, in contrast to area and length?


*In short: is it because volume is not quantized?
 A: Obviously:
$$
A_{\text{P}} = \ell_{\text{P}}^2 = (\ell_{\text{P}}^3)^{\frac{2}{3}} \equiv V_{\text{P}}^{2/3}.
$$
So any expression that involves the Planck area could be expressed in terms of the Planck volume instead.
But notice that the internal volume of a black hole is hard to define, since there's no static observers inside.  Only the external area has a meaning.  So I don't see why you would prefer to have equations with the Planck volume, which doesn't have a well defined physical meaning.
One situation which I know the Planck volume may have some meaning is the Einstein-Cartan theory with torsion (or ECSK theory).  In that theory, the Dirac equation have an extra "contact interaction" term.  The Planck volume $V_{\text{P}}$ doesn't shows explicitely in that term, but the Dirac field density enters the interaction term and imposes a limit to the energy density.  You may want to check the literature on that subject, but be aware that the mathematics are extremely heavy when you add torsion to General Relativity.  It is quite disgusting!
