The restoring force is electromagnetic in origin, having to do with atomic/molecular interactions.
Both electrostatic as well as magnetic forces vary inversly with the square of distance.
$F_{_{EM}}\propto \cfrac{1}{d^2}$
So why does the restoring force vary directly with the length of the spring?
$F_{s}\propto x \implies F_{s}=-kx$
PS
In this question it has been said that applying force on the object does try to displace atoms away from each other so electromagnetic forces should reduce.
Hooke's law is an approximation good for small values of spring deflection. Here is why it's a good approximation:
In a chunk of material being pulled in a tensile test, the pull force is very tiny compared to the sheer number of atoms in the test sample. This means that the atoms in the solid are deflected by the external stress from their equilibrium positions in the lattice by a very very very tiny amount.
A simplified linear deflection model works very well in this case, even though the electrostatic force is not linear with distance.
Metals don't stretch by moving apart: they stretch by moving sideways. Atoms move tangentially to their bonds. Strain at the lattice level is not aligned with strain at the macro level. Look at a failed test sample: both the ductile and the brittle failure zones exhibit failure on the slip plains, not on the orthogonal plane.
The Hooks law applies to elastic material or springs. Their electrostatic configuration doesn't change during loading and unloading.
They have their fibers unwinding or crystals straining or other linear strain-stress relations.
Interaction at the molecular/electron level in the sense you referring produces resistance at orders of magnitude higher. those are the forces that keep us on the surface of the earth on our feet, or in a hard car collision don't let the opposing car's molecules get penetrated by the other car. (they just smash each other).
An example of an exception to elastic behavior could be an artillery explosion: the impact converts a huge amount of kinetic energy to heat so it can melt and burn and chemically change the armor and render it weak.
It does need to. The springs you are referring to are designed specifically to have the restoring force linearly vary with elongation. It doesn't need to.
