Is not US air force most less important part in US Military?

Air force generally deals with air warfare and air to ground bombing. How ever US Navy planes and US Marine planes also take part in air war fare from achieving air superiority from strategic bombing Air force neglects air to ground attack so it is left for attack helicopters of Army and Marines. So it is clear that air force is not alone who only deals with aerial matter. In Gulf war US navy and Marine planes also bombed Iraq, 1980's clash with Libya air force played minimal role, US Navy planes clashed with Libyan planes achieving air superiority and also bombed Libyan bases. Air force neither have additional arm like Army has Army Aviation, navy's Naval air arm and Marine's marine air arm. So what air force actually does??