Natural units are in common use in many areas of theoretical physics. In these systems
$$ c = 4\pi G = \hbar = k_B = e = N_A = \alpha = 1 $$
One major fatal flaw of these systems is that they are based on a very bad system, the SI unit system. A further improvement to this system can be made if one decides to use a time-tested unit system, the US imperial unit system.
The speed of light in US imperial units is a striking example of its superiority over SI. In SI, the speed of light is defined to be 299,792,458 meters per second, or 0.299692458 meters per nanosecond. Since the meter is about 3.28 ft, the speed of light is 1.0166816 feet per nanosecond.
Therefore we define one planck foot to be 1.0166816 US imperial feet. Then the speed of light is exactly one planck foot per nanosecond.
This system has the benefit that the natural units are still comprehensible to the average person (American). Further extensions to this system can define planck jiffys (time), planck slugs (mass), and planck farenheit.
If you defined 1 mol as the amount of molecules are in one mol, then Avogadro’s number is 1.