The dimensionless fine structure constant, alpha ~= 1/137, is indeed one of the important keys for unlocking the underlying nature of physical reality. Feynman's quantum field theory uses perturbation expansions based on factors of alpha and the gyromagnetic ratio calculated with such a QFE series is the most accurately known physical constant of nature.
The problem with alpha is not that there is no way to describe it...the problem is that there are any number of ways to describe alpha since it is dimensionless.
My favorites are as the product alpha x c is the average velocity of the electron for a hydrogen atom as well as alpha / c is the velocity of spin at the elementary charge radius of an electron or proton. That means that the charge velocity of the electron in hydrogen makes a magnet that interacts with the magnet that comes from the charge velocity of the electron spin. This spin-orbit coupling is what splits the s and p orbits of hydrogen, which have different average velocities, and that is what causes most of the spectral splitting of S and P states of hydrogen and other elements.
The constancy of alpha from spectral splittings in both distant galaxies and precision atomic clocks is the only argument for an expanding universe of unvarying constants. Any theory that supposes forces are different in distant galaxies must somehow explain why alpha appears to be constant for both distant galaxies as well as for precision atomic clocks.
In fact, it is not really alpha that appears to be constant, it is really alpha^2. In a shrinking universe, this key fact means that alpha does vary in distant galaxies and alpha^2 only varies as a second order. In fact, there are many reports of the second order variation of alpha^2 and atomic clocks are only now precise enough to begin showing these second order effects.