No, for a short while in the 80s as Hornets replaced A7s some carriers, JFK and Ranger definitely and I think America and another did cruises without the A7 squadrons. It had something to do with the catapult needing modification to accept the Hornet, it wasn't a big refit but the schedule meant that several carriers did cruises with a second Intruder squadrons rather than the two A7 squadrons, Marine A6 squadrons had to go to sea to make up the numbers. So aside the cats and dogs which RN carriers also had in their own form at this time USN carriers core airgroup was 48 aircraft, not the usual 60 which required 4 cats and lifts.
They did, but were removed in the 70s.
What needed to happen was Parliament too stop carrying on about tonnage, why they cared that it was 53,000t rather than 57,000t is beyond me, and maximise the aircraft operating ability at the expense of secondary stuff like Sea Dart even though it did put them out of step with carrier design at the time.