I'm just wondering why the current density $J$ is always defined as the amount of electric current traveling per unit cross-section area $J = \frac{I}{S}$, and not per volume unit $J = \frac{I}{V}$ so $\frac{A}{m^2}$ instead of $\frac{A}{m^3}$. Wouldn't it be useful to calculate electric current density per volume?