Why arsenal ships run into a missile inventory problem

What are the strengths and limits of an arsenal ship built largely around vertical-launch cells?

The concept is attractive, but its value depends on producing enough missiles to fill and sustain it.

An arsenal ship concentrates a large number of vertical-launch cells in one hull. Saturating an opponent's defences is one proposed use, raised through a fictional example. The reservation is whether a navy could build enough missiles to fill and sustain such a ship. A novel can assume that stockpile exists, while a real fleet has to provide the weapons.