The Air Force would probably pay for Marine F-35B's before they buy their own. They aren't organizationally flexible enough to actually take advantage of forward basing, and it just adds another training and supply chain to incorporate. If they had oodles of new money to develop those concepts, then sure, it makes some sense. They don't and, barring major changes, won't.
Not sure the Marine plan of trying to play a shell game with FARBs and a $90m stealth fighter is a great plan anyway, but I do not see the Air Force having an appetite for funding it.