I always felt that F-35B at least should have been its own design. As for A & C, there have been successful examples of naval aircraft being used by air forces too - such as F-4, and F/A-18. But trying to have a design that is also STOVL capable?
But for the obvious reasons they vastly prefer two engined planes, plus I've read the F-35's single engine is so big their current logistics system will have trouble getting new ones to a fleet at see, I assume this means it can't fit in a C-2 or maybe V-22.