Marine aviation is very small, and they are naval aviators, so Marine squadrons do carrier duty. But they are small and mobile, and want to be able to operate from remove patches of dirt. Helicopters in general, and the F35B and V22 in particular are principle enablers of CAP. And Marines generally do not want Air Force over them as they tend to prefer Army and Naval aviator brand of CAP.
The Army is not allowed jets per the same post WWII regulations that separated the Army Air Corps to form the Air Force service branch.