Missile stock depth in a long naval war

Do modern navies assume both sides will run out of ships before they run out of missiles?

No; missile stocks are limited, and defeating a heavily defended carrier group can require exponentially more weapons than attacking one ship.

Available missile stocks are smaller than popular impressions often suggest. A single undefended ship and a carrier battle group impose radically different attack requirements because the latter combines detection, deception, interception, and layered defense. Saturating that system can demand many weapons for each potential hit. The exchange reframes lethality around campaign inventories and salvo economics rather than the power of one missile.