Read my comments again last time when aircraft carriers came face to face was durring cold war. At that time there was no concept of long rang BVR systems. Now a barrage of 5-6 cruise missile and all will be left is a carrier with massive holes. China and Russia are developing them to project power just like US. Any ways that is just my opinion. Also if china manages to perfect accuracy issues of carrier killer ballistic missiles then there wont be any place for them to hide.
NO carriers came face to face post WW2. In the context of the cold war, I assume you are making reference then to the advent of the Russian Kiev class (first of class commisisoned 1975) and the Yak-38 (entered service 1976), equipped with the 8km range, infrared homing AA-8 Aphid sr-aam. With their heavy ASW orientation, these 'heavy aircraft carrying cruisers' were never intended to face off with USN CVs or CVNs.
Anyway, regrding BVR, what do you think Navy's 1960s F4 Phantoms were equipped with, besides the 5km AIM-9B Sidewinder infrared homing missiles? Heard of the 32km semi-active radar homing AIM-7C Sparrow aka AAM-N-6 Sparrow III) ? That tarted development in 1951 and entered service in 1958 and was put on the Phantom when it was introduced in 1960. A major improvement over the F-8 Crusader, which had used AIM-9 Sidewinders in both IRH and SARH versions.
Early beamriding Sparrow versions had been employed on a limited number of a few other navy jets, e.g. the Douglas F3D Skyknight all-weather night fighter (1954), the McDonnell F3H Demon (1956) and the Vought F7U Cutlass (1956) used AIM-7A (Sparrow I aka AAM-N-2). The active radar homing AIM-7B (Sparrow II aka AAM-N-3) was intended for used on Douglas F5D Skylancer (4 built) and the Avro Canada CF-105 Arrow (5 built) but never saw service
Further, note that of the USNs wartime 24 ship Essex class (many of which served post WW2 well into the Vietnam era),
none were lost while two, USS
Franklin (CV-13) and USS
Bunker Hill (CV-17), came home under their own power and were successfully repaired even after receiving
extremely heavy damage.
Essex class carriers hit by Kamikaze weapons were often launching and recovering aircraft again in less than two hours.
Perhaps you should also acquint yourself with the carrier fire incident on the USS Forrestal (1967, 7x 1000lbs bombs cooked off on deck) and the USS Enterprise (1969, 18x 500 lbs bombs cooked off on deck). In both cases, due to fire, multiple 500lbs and/or 1000lbs bombs exploded on deck and blew holes through the armored flight deck, to up to 6 decks down, through which burning aviation fuel spread into the interior. In both cases, crew managed to put out the fires and save the ships within 16 hours, after which the ships continued under their own power. Likewise the hangar deck fires on USS Boxer (1952) and USS Oriskany (1966). These incidents not only demonstrated the damage and fire control capabilities in the USN on carriers show but also helped improve them as well as the design of carriers like the Nimitz class.
To this day, only the USN has conducted tests with nuclear devices against carriers (and other ships) in operation Crossroads and a life fire excercise on a decommisioned carrier (the Kitty Hawk class USS America, 2005), which provided valuable lessons incorporated into the latest USN carrier design, the
Gerald R. Ford-class aircraft carrier (CVN 78).
See also:
https://fas.org/man/dod-101/sys/ship/docs/98-217.pdf (ch. 5)
http://lexingtoninstitute.org/wp-content/uploads/aircraft-carrier-invulnerability.pdf
By comparison, the Russian navy suffered mostly boiler explosions and engine room fires on most of its flat tops (1 of 2 Moskva class, 3 of 4 Kiev class, Kuznetsov) and a single rough landing of a Yak 141 on a Kiev.