It's not always meaningless. For example, we may talk about the change of the mass of a human (in kilograms) after a diet.
But the point is that the value of a dimensionful quantity – and its change or constancy – depends on the magnitude of the units and they're matter of conventions which may change, too. So an increasing numerical value of $\hbar$ could be just to a decreasing value of what we call one kilogram. We define e.g. one kilogram using the international prototype and consider it a "constant mass" while the mass of a human on diet is more variable.
In this comparison, the constants $\hbar,c,G$ are even more naturally constant than the international prototype. In fact, "adult" physicists use units where $\hbar=c=1$ (quantum relativistic units) and sometimes also $G=1$ (general relativistic units or Planck units when all conditions are imposed). So $\hbar,C,G$ can't really change when natural units are used because they're always equal to one.
Even if we use more everyday units in which the numerical value isn't one, it's still better to define such units in such a way that $\hbar,c,G$ are constant. In fact, one meter is already defined so that $c=299,792,458$ m/s at all times. It's not quite the case for $\hbar$ and $G$ yet but this may change in the future.
Because $\hbar=c=k_B=1$ etc. are so natural, it makes sense to consider the constancy or variability of all other dimensionful constants by the constancy or variability of these constants converted to the natural units.