If you would treat a nucleus of general shape without using a multiple expansion, details about this shape would be lost and the nucleus would be treated as being spherically symmetric.
Correction: after reading the other answers, I realise I was completely wrong and that the main complication would be that the calculation of the perturbation (matrix elements) would be extremely hard to calculate without splitting everythin up in the multipole expansion first.
This reply was modified 4 years, 3 months ago by ErwinVanBuylaere.