You mean having a STOVL variant that can also be catapult-launched?Would here have been any merit in having a CATOBAR F-35 that could accept either the conventional F135 engine or the lift-fan version thus allowing more flexibility?
If so, I think the weight penalties required to make it more robust to handle the stresses would be severe. Also, that would open a can of worms i.e., start a serious discussion on the case for big-deck CATOBAR ships.. maybe build more LHA-6 types instead. Definitely no where as capable but more affordable.