Bought by the Marines?
They will be bought (designed, manufactured, upgraded, depot-maintained and supplied with spares and crew training through-life) by the US taxpayer, via the same Department of the Navy budget as every other DoN aviation asset, including the AV-8 and MV-22.
The DoN and the command chain above it therefore has the duty and right to decide where the aircraft go, and what they do. If that involves putting Marine-crewed/badged CV aircraft on CV decks, so be it.