Would the battleship's VLS battery be used mainly for strike or for air defense?
Short answerBoth: hundreds of cells allow a layered mixture of quad-packed local-defense missiles, long-range interceptors, and strike weapons.
NotesThe answer uses the hull's scale to escape a forced choice between offensive and defensive loads. Quad-packed Sea Ceptor could provide a very large close-defense inventory, longer-range Aster-family weapons could supply area defense, and remaining cells could hold Tomahawk, SCALP, or comparable strike missiles. Additional deck-launched anti-ship weapons could broaden the mix further. A magazine this large lets commanders tailor offensive and defensive proportions to the deployment instead of accepting the severe cell scarcity of a smaller escort.