I am personally not sure if i understand the question for 100%, but here is my answer anyway.
When you want to use perturbation theory, what you want is a simple hamiltonian with some small corrections to it. The multipole expansion of the nucleus is exactly this: it breaks down the problem in a simple thing, plus some small corrections. So what i’m trying to say is: if you don’t do a multipole expansion of the nucleus first, then what would you use as useful perturbations to describe the coupling of the nucleus to the electrons? If you would start from a general nucleus (so no expansion) this coupling would get really complicated.