There are too many questions mixed together here; I'm going to try to separate them out.
First, there is the error I addressed in my comments; the Marine Corps existed before the United States did. They are the oldest military service in the US military. For a brief history of the US Marine Corp, see Marine Corps. I'm a REMF, and a Navy REMF at that, so I'm going to defer to them on their own history.
Second, there is the question of whether they have any value? Whether they have ever saved the day. I strongly suggest that you not ask this around a Marine; I try not to insult people who make a habit of charging into machine gun fire. There are many possible responses, but I would suggest that you might want to google terms like Shores of Tripoli or perhaps China Marine, or John "magnet ass" Glen.
Third there is the question of why we have Marine Aviators. There is legitimate debate on this topic, but different services and different missions have very different needs for air support. Marines need close air support that is tightly integrated with their ground forces. Integrated Marine aviation provides that better than the Air Force does. I've got lots of friends and relatives in the air force, but even the best air force pilot doesn't understand the need for support to ground troops the way a Marine does; the Marine in that cockpit is both a Rifleman and a pilot. Every profession has specialists. You might as well ask why the Department of Defense needs a payroll office; after all the Bureau of Indian Affairs has payroll clerks - they could clearly do the job right? Or why do I need an internist an orthopod and a neurosurgeon?? They all graduated from medical school right?
Finally there is the question of whether we should have a unified military service (like the Canadians), or a branched military service (like US and UK and many other nations). That's not really appropriate for History. The answer to that question is entirely political. There are entrenched stakeholders who prefer things the way they are, and that kind of reform simply isn't the highest priority. Changes to the military are very costly -both in terms of dollars and mission effectiveness. Unless there is a compelling reason to make the change, it probably isn't a good idea.
@korvinStarmast adds an excellent point, which I'll include here to avoid deletion:
Form a purely military point of view, the Marines are the only force that inherently does combined arms warfare as part of its make up. The Marines were Joint before Joint was a thing, by about 50 years. (See development of Close air Support and Amphibious doctrine in the interwar period. )
Postscript - as Rodrigo de Azevedo points out,
. . . all USMC aviators undergo infantry training. Thus, when providing close air support, the USMC aviator may be friends with the platoon or company commander on the ground.
every Marine is a rifleman. Aviators undergo infantry training, and I believe maintain the qualification. Although that doesn't seem to directly address the OP question, it actually highlights the difference between the Marine perception of what it means to fight a war and OP's. It is a perspective on combined arms.