The F-14 wasn't just an air defense fighter. Any multirole would work for a carrier-on-carrier fight, winning through numbers and training. The F-14 was designed to counter a specific threat: Tu-16s and later Tu-22Ms armed with long-range anti-ship missiles. The Soviets had dedicated an entire branch of the military to countering USN ships with aircraft and air-launched missiles.
Only the F-111B could patrol far enough out, intercept fast enough, and carry sufficiently long-ranged weapons to engage these bombers before they could release their payload. The technology of the 1960s (or even the 1970s-1990s) wasn't capable of intercepting such missiles once released.
The F-111 Aardvark had even more problems than the F-14A. It was too heavy, difficult to handle, and could barely fit on or operate from a carrier. Adopting the Tomcat was by far the lesser of three evils. The third, least desirable option would be to keep out of range of land-based aircraft. More on the F-14's design compromises in this question.
With the Tomcat's phase-out and retirement in the late 1990s-2000s, the USN has lost the capability to intercept missile-armed bombers at standoff range on its own. This capability has since been replaced by:
- Ending the Cold War. At the time, it was believed the threat wouldn't be relevant for many decades. The rise of China had perhaps been underestimated.
- Diplomatic treaties. START, SALT II, and CTR have targeted the Tu-22M for capability reduction, dismantling, and export restrictions. Only 66 out of the original 500 can fly today.
- Improved AEW radars on the E-2D, increased E-3 coverage through allies, and more spy satellites give earlier warning against an incoming strike, giving slower fighters time to intercept.
- The SM-3 and SM-6 missiles, which have anti-ballistic capabilities, and could intercept some, though not all, incoming anti-ship missiles.
- The Meteor and to a lesser extent the AIM-120D approach the AIM-54's range, and their better guidance should compensate for smaller warheads.
- Electronics export restrictions are being reintroduced, to slow down a re-emergence of the threat on the same comparative level that it was pre-1991.
While no one point is a complete replacement, they work together. Better avionics, improved C5I, more NATO-stationed forces can compensate for the loss of dedicated capabilities. The threat itself has also diminished greatly; it will be a while before China can catch up to the late Soviet capability level.
The Super Tomcat was an industry proposal. The Navy didn't ask for it by name; they weren't happy with the original. Even the boldest proposals still point at a maintenance-intensive, non-stealth aircraft, with a moderate air-to-ground payload compared to its weight.
The F-14 was indispensable against the Tu-22M, while also being a good general purpose interceptor. Swing wings aren't needed for simple bombing runs. At the same time, it's likely to be inadequate against the J-20, H-20, or a possible new J-20 or PAK FA/DA/etc derived naval strike bomber. These stealth aircraft can be countered by getting close through better stealth, where the US still has a lead, wide-cast UAV nets, SIGINT, and/or intercepting their payload with even better missiles.
Had the Tomcat still been around, it would've been modernized to some E, F or G variant. It's not likely that the USN would've chosen to spend more on it than necessary. Update the avionics to work with modern munitions, put in more glass, use a curved windscreen and a regular HUD so the pilot can see in front of them. The Super Hornet is 40% larger than the original; there's no room to enlarge the Tomcat, itself designed to only-just-fit on a carrier.
So a Super Tomcat wouldn't be inevitable. Even in absence of the Hornet, the Navy would remain very keen to get a further improved, faster, longer-ranged F-35C. They could even support a naval F-22, had the recent political escalations happened while the Raptor was still in production. Stealth has become the new speed, though it's still only one capability.
P.S.
While it's only a simulation, the sim group Grim Reapers has run through some scenarios of such a strike, and a full complement of F-14's came the closest to saving the carrier. Similar results have been replicated in Command: Modern Operations, and no doubt many times before by actual military researchers, prompting the Tomcat's development and then retirement. Per this simulation, the remaining Tu-22M fleet is only enough to take down one CSG. Even though the missiles have improved, the bombers haven't changed much.
