I think F414s, even maxed out in their development, aren't going to be enough power for an ~80,000lb aircraft expected to do fighter missions in addition to striker, while F110s are.
Where am I getting ~80klbs? Carrier limits. Max takeoff weight is limited by the steam catapults because we're going to have Nimitz classes in service till ~2050. Max landing weight is limited by what the arresting gear can stop, and IIRC the Ford-class Advanced Arresting Gear isn't capable of much higher weights, it's capable of safely stopping much lighter aircraft (as in UAVs/CCAs).
Weight wise, the MTOW of a Tomcat is ~78klbs, the KA-3 "Whale" was ~83klbs, and the F-111B was up to 88klbs. Since we're unlikely to have swing wings to help out low-speed handling, so something in the 75-85klbs range is not unreasonable to launch.
But the trick comes from the landing weight. Recovery weight of an F-14 was 55klbs, it's why they so rarely flew with 6x Phoenix missiles. They'd have minimal fuel left, Tomcat pilots said it was "make your trap on the first pass or hit the tanker". So that says what our "Empty weight plus weapons weight plus ~3000lbs of fuel" can be. I'm assuming a weapons load for the FAXX as roughly equal to the ATA (possibly with more AAMs): ~12,000lbs in ground-attack mode, ~9500lbs for 4xSM6 and at least 2xAMRAAM, and 5-6,000lbs for pure AMRAAMs.
55-3-12=40klbs empty.
And a reasonable rubric for MTOW is 2x Empty Weight (checks with pretty much every jet from Teens on up). That means 80,000lbs ish MTOW, which checks with catapult max.
80-12-40=28klbs of fuel onboard.