Why use gauss law?

First of all we use Gauss's law because it is a law of nature! Second: Gauss's law (together with ∇×E⃗ =0, which is only strictly valid in electrostatics) is equivalent to Coulomb's law for the electric field of a distribution of charges. You can prove one from the other. Third: You a right about external fields cancelling. Gauss's law essentially says that electric field lines only end on charges. So if you have a volume that doesn't contain a charge, any field line which enters will also leave and the total flux through the closed surface is zero. Fourth: In the sphere problem is the sphere a conductor? If so it screens anything happening outside the sphere. If the sphere is not a conductor then the field inside will depend on what is happening outside, but the total flux through the sphere will only depend on what's inside.

Since it is very fundamental law