For a may electron atom, a closed subshell structure implies $$L=S=0$$ and therefore also, $J=0.$ Therefore, the ground state wavefunction of such an atom is spherically symmetric because the rotation operator does not alter the state. I understand this mathematically.
But physically, why should this be true? If we consider the Neon, it has the ground state electronic configuration $1s^22s^22p^6$ i.e. the outermost orbitals are $p_x,p_y$ and $p_z$ none of which are spherically symmetric.