The "fundamental constants" (maybe c, h, G, k, ...) are just artifacts from starting out with, from a fundaenntal physics perspective, bad units, and redconning the theory.
If we consider, for the moment, physicial theories, expressed using math, with a notion of time (consider t), then you have "rate" (consider n/t). For periodic processes, that's the same units are frequence. The Schrödingerequation speaking about "energies", but sets them up just as multiplies of the lowest frequency (technically, a diagonalizable operator where all eivenvalues are some real multiple of a lowest frequency).
If you have light moving at constant speed, any t corresponds to distance traveled, so distance is captured in units of t just as well. Force is a spatial energy gradient, so 1/t^2. Mass is energy, i.e. 1/t too. Newtons F=m*a works out find with just that, where acceleration has units 1/t.
"Entropy" ought to be just the log of the volume in a configuration space. You can multiply it with any energy to get the entropy from theormodynamics. The Boltzmann constant does this job.
Pic only semi-related, even most professional physicist aren't willing to give up "length" as a conceptual seperate unit, even if you only ever need time for anything.
Of course, if you go about with a ruler you come up with feet or inches or even centimeters and not think about light traveled, and if you stare at a light bump long enough, you come up with lumen and lux and all the brighness and radiance and light related units that obscrue the physics. In the end, there's really just time (or space, in any case it's t) and rates 1/t (frequencies, or even rates of rates, e.g. power). t and 1/t^n are relevant for physics. The rest is historical conversion factors.
