It is like this: dV = -E(vector) dot dS(vector)
When you take the dot product of the electric field vector with the
direction vector you get a scalar quantity and that is the voltage.
Basic vector calculus,
the dot product of two vector quantities is a scalar quantity.
In short because the mathematics of the physics required it.
If the question is regarding scalar electric potential, V, vs. vector
magnetic potential, A, it can probably be attributed to the extra
degrees of freedom that come from magnetism being nothing more than a
relativistic correction of electrostatics. Because relativity
includes velocity, a 3-D vector quantity, magnetic potential probably
is vector simply because velocity is added into the mix.
MM