In the Newtonian sense, "mass" is representative of a body's general resistance to motion. Einstein derived $E = mc^2$ but it was in the context of the amount of mass lost after a body emits some amount of light with energy $E$. In that context, $m$ is more like a $\Delta m$. Another interpretation of $E = mc^2$ is, for a body of mass $m$, $E$ is the total amount of *electromagnetic* energy you could get out of it if all of its mass were converted to light radiation.

Both interpretations of $E = mc^2$ seem to refer to specific thought experiments/hypotheticals, and it seems that $E$ always refers to the energy carried by light in any of these interpretations, so we are constrained to conceive of it in that way.

My question though is: is it possible, since we do have a relation between $E$ and $m$, to simply eliminate the concept of inertia entirely? For example, why not just substitute $\frac{E}{c^2}$ as $m$ into ${\bf F} = m{\bf a}$ and work instead with energies, forces, and motions? In this setting, we have to conceive of energy as "the capacity for a body to perform work on its surroundings," rather than a constant of motion that arises from a time-translation symmetry. "Mass" becomes a potency for a body's ability to both create light and perform work.

Wouldn't this eliminate a concept ("mass," whatever it is) and streamline the theories? But maybe the classical interpretations are just more attractive over thinking in terms of potency all the time. Not to mention the practical aspect of having extremely large numbers to work with once the speed of light is baked into all the equations.