Question

why should electrostatic field be zero inside a charged conductor?

Answer 1

in electrostatics free charges in a good conductor reside only on the surface. So the free charge inside the conductor is zero.So the field in it is caused by charges are on the surface.Since charges are of the same nature and distribution is uniform , the electric field cancel each other.

Answer 2

Hey !!

In the static equilibrium, there is no current inside, or on the surface of the conductor, hence the electric field is zero anywhere inside the conductor.

ALTERNATIVELY

Since, the charge inside the conductor is zero, the electric field is also zero.

Good luck !!