We've used the Harriers STOVL ability in Afghanistan early on in the war. There were some airfields that were completely bombed out, only helos and Harriers could use them until the runways were fixed.
We also used the capability during the march up to Baghdad. Harriers landing next to helos along the highway at FARPs. Oh, and that whole feint thing in Gulf War 1, where we had the entire 1MarDiv sitting off of the coast of Kuwait in amphibs, giving the Iraqis the idea that the Marines were coming across the beach dividing the Iraqi military and forcing them to deploy on two fronts- giving Gen Schwarzkopf's swinging door strategy even more leverage.
However, we regularly use it off of the small deck carriers. Why do we need it? Because the whole purpose of a MEU is to have a completely organic combine arms fighting unit (A Marine Air/Ground Task Force- MAGTF), complete with it's own Ground, Logistics and Air combat elements (Hence the GCE, ACE, and LCE) MEUs (and their expeditionairy strike group) deploy separately from a CSG.
The same reason that we Marines need the F-35b is the same reason the Navy and the Air Force need their model. The game is changing, if we have to escort a flight of MV-22s feet dry we need to ensure the way is clear for them so they make it to their destination. With emerging SA threats, and the places we may go I sure as shit don't want to do that in a Hornet, much less a Harrier. With the current fiscal climate in the military we can't afford the luxury of purpose built airplanes anymore. Therefore the F-35 has to be able to do everything that we need a tactical fixed wing airplane in support of the MEU to do. That means OCA to support a TRAP mission, DCA to protect the ESG, deep/stealth strike to take out those new and robust SA nodes, EA to send trons down range so those helos/Ospreys/and other F-35s flying through that SAM WEZ don't get shot down. We fly ISR regularly (ATARS) And of course, what is near and dear to the Marine Aviators heart- CAS. And we have to be able to do it from where the MEU is- onboard a ship that doesn't have catapults or arresting gear.
The bottom line is that we do a lot more than what most people think, we bring a lot of capabilities to the fight so that battalion can be there ready to kick the teeth in to anyone to who needs it anywhere in the world. We are self sufficient for as little as 14 days to as many as 30- that gives the AF, Army, and Navy enough time to mobilize and get their shit together to bring in the serious heat. We aren't designed to be a second land Army (though we were/are used as one in Afghanistan). We are the step between the SOF guys and the big Army.
If you don't think we need that, or you think that the AF could do better, or think that we don't need the Marine Corps all together, then join the club of naysayers. There are a lot of them - even in congress. The Marine Corps has survived worse times, and has had to defend itself and it's existence many times. Yet we always come out on top? Why? Because while America may not need a Marine Corps, America wants a Marine Corps.
Today (November 10th, 2013) marks 238 years of the United States Marine Corps. We celebrated our 101st year of Marine Aviation on August 20th. We aren't going anywhere, we aren't going to give up any capabilities, and we aren't going to relinquish the ACE over to the Air Force.