Why a navy might pair CATOBAR and STOVL carriers

Why build a STOVL light carrier and custom aircraft instead of a smaller CATOBAR carrier using the main fleet's aircraft?

Because the light carrier may be optimized around amphibious forces, where commonality with rough-strip and marine aviation matters more than matching the strike carrier.

An LHD supporting amphibious forces can share aircraft with marine aviation and rough-strip operations. That relationship can matter more than sharing an air group with the main CATOBAR carrier. Maintaining separate air groups can also prevent aircraft being drawn back and forth between different duties. Britain's original concept paired two Queen Elizabeth-class carriers with three LHD replacements for Albion, Bulwark, and Ocean. All five flight decks could have operated the same F-35B aircraft, giving a medium power flexibility across its global commitments. The loss of that wider force plan makes the eventual aircraft choice harder to understand when the surviving carriers are considered alone.