That would certainly make the Air Force scream. However, they discarded the old name, so "U.S. Army Air Corps." is the logical name for Army aviation. This might be a good time to float the idea, too - "retro" is "in".
An updated version of the A-10 might be something to consider, but the F-35 ain't it. The designers can look at all the battle damage data from the two Gulf Wars and correct any weaknesses exposed by that enemy fire. While they're at it, make the new version with a 2-up cockpit, like the F-15E Strike Eagle. Let the pilot concentrate on flying and engaging the enemy with the gun, while the co-pilot (both should have full flight controls and instruments) handles the other weapons systems and anti-SAM countermeasures.
Such a 2-place design would make the aircraft even more lethal and better able to survive in the hostile environment that is close air support.