For any body we have $E = mc^2$, where $E$ is the capacity of the body to do work on its surroundings and $m$ is the resistance the body has to move from its state of rest. Therefore, the capacity to do work is proportional to the body's inertia. It would seem at first glance that these properties should be unrelated.
Why can't we have a feather-light body which is very potent in its capacity to perform work on its surroundings?
The premise isn't quite correct; we could write $E=\sqrt{(mc^2)^2+(pc)^2}+V+E_0$, where $p$ is the momentum, $V$ is potential energy, and $E_0$ is a constant that sets the reference zero.
At small speed $v$, this simplifies to $E=mc^2+\frac{1}{2}mv^2+V+E_0$. Thus, we could do work by converting matter to energy, by slowing the body, or by allowing the body to move to a lower potential level. Electrons, for example, are light but can provide work when allowed to move in an electric field.
Why can't we have a feather-light body which is very potent in its capacity to perform work on its surroundings?
In batteries such thing as mass energy density is important. The unit of mass energy density is J/kg.
There are different batteries with different mass energy densities, made of different materials.
But what is mass energy density of energy? Let us calculate:
Energy of energy is $E = mc^2$ And mass of energy is $m$.
To get mass energy density we divide energy of energy by mass of energy: $mc^2 / m$ = $c^2$
So it happens to be so that there are no different energies with different mass energy densities. Energy is always made of energy, and always has mass energy density $c^2$. Which I do not find surprising at all.
