Formalism for Unit Consistency

I was thinking about how the propagation constant for Transmission Lines looks like this:
${displaystyle gamma =alpha +ibeta}$ , and here the units for $beta$ is $frac{radians}{meter}$ and the units for $alpha$ is $frac{neper}{meter}$, I understand ‘why’ this is done, because the $beta$ in reality signifies phase constant of the wave so it is a measure of $frac{angle}{length}$, and $alpha$ represents the attenuation constant so it is a measure of $frac{attenuation}{length}$, and we are technically allowed to add them since Np and Rad are both unitless measures.

I was wondering if there is a more formal justification or reason as to why we do this? More generally is there some more rigorous structure for all of the "rules" of units?