John P. Ralston might have an answer for you, he proposes (https://arxiv.org/abs/1203.5557) "a modern approach where Planck’s constant is absent: it is unobservable except as a constant of human convention... In the new approach Planck’s constant is tied to macroscopic conventions of Newtonian origin, which are dispensable."
Case in point, the quantization condition:
$$
[x, p] = [x, -i\hbar\partial/\partial x] = i\hbar.
$$
"Introducing $\hbar$ made the first time in history where multiplying a
math identity by the same constant on both sides was reported to
make a new physical principle". It comes from
$$
[x, -i\partial/\partial x] = i,
$$
which is the trivial identity it appears to be.
Exhibit 2, the path integrand of massless Dirac spinor:
$$
e^{\frac{i}{\hbar}S_{Dirac}} = e^{\frac{i}{\hbar}\int i\hbar \bar{\psi}\not{\partial}\psi} = e^{i\int i\bar{\psi}\not{\partial}\psi}.
$$
If the two $\hbar$s net out, why do we bother to introduce $\hbar$ in the first place? As for the mass term in Dirac action, $\hbar$ can be simply absorbed into the redefinition of mass $m$.
Exhibit 3, the fine-structure constant:
$$
\alpha = \frac{e^2}{\hbar c}.
$$
Measurements of $\alpha$, $c$, and $e$ seem to get you $\hbar$. The catch is that the whole schema hinges on the convention of unit of electron charge
$e$ and measurement thereof. If you do proper rescaling of gauge field
$A$ in the QED path integrand, only the fine-structure constant $\alpha$ remains. Electron charge $e$ drops out completely and you don't need $e$ anywhere in the Lagrangian. We don't sustain any loss of information if we abandon the notion of $e$ and only invoke $\alpha$ in theory and in experiment (thus foregoing $\hbar$ as well ). Planck constant $\hbar$ is only an arbitrary intermediate step which is subject to human convention.
An added note. When you do rescaling of certain field and then a parameter changes size or pops up at a different Lagrangian term, it’s a change of physics unit. However, if two parameters in a theory collapse into one parameter after rescaling ($\hbar$, $e$ -> $\alpha$), you might suspect there must be something fishy and redundant, which is nothing but the Planck’s constant $\hbar$. Given the historical role $\hbar$ played, physicists have a certain emotional attachment to it. And the widely circulated folklore surrounding $\hbar$ lends it a mystical aura of importance. It’s not surprising that the view expressed here in this thread would receive plenty of down votes. But if you pause for moment and think twice about it, you will be rewarded handsomely by the insight gained.
