I stood (OK, sat) thousands of hours of watch in CIC on 2 Aegis ships, one a cruiser exactly like the Gettysburg. I was CSC, and directly involved in air defense engagements. You are correct. CO and whoever the TAO was are probably done, along with the specific watchstanders that made critical errors. It's also quite probable the Carrier was in the loop throughout the incident.
Fortunately, everything is recorded, so the entire engagement within the Aegis system is recorded, as are the internal and external voice nets the watchstanders were speaking on. From the description of actions before the FF incident was reported, the Gettysburg was engaging drones and anti-ship cruise missiles at the time. Of course, as soon as they realized they shot down an F-18, the flow of information to the public stops. It sounds like the "ASCM" was actually our F-18.
I was just before aegis. The last of the moveable antenna. The process was the same. Many mistakes to shoot a friendly. Thank God those men survived.