Gauss's law is universally true, yet physicists call it useful in only a handful of geometries. What underpins this distinction when computing an unknown field?

C. It yields the field directly only when symmetry makes its magnitude uniform over the surface

Gauss's law always balances net flux with enclosed charge, regardless of exterior sources or curl. But extracting an unknown field from the integral requires sufficient geometric symmetry to treat the field magnitude as constant across the integration patch.