I don't think that's necessarily inevitable. None of the British carriers was sunk during the Falklands war, despite the Argentines having diesel subs and exocet missiles.
None of the British carriers was sunk during the Falklands war
Yes and no. The Atlantic Conveyor, a makeshift helicopter carrier, was sunk, taking the UK’s Chinooks with it, leading to the famous “yomp” across the island. But you are right that both of the Harrier carriers were OK.
Ah, yes, fair enough, but of course the Atlantic Conveyor neither didn't have the defenses of a modern carrier, and wouldn't have been as much of a defense priority.
Note that the Argentinians started the war with only five air-launched Exocet missiles in stock and with those they took out an air defence destroyer and a very important supply ship.
The Argentinians deployed two submarines. The Royal Navy caught the WWII surplus Santa Fe. The more up to date San Luis evaded the RN and it's attacks were only foiled by poor maintenance of it's weapon systems.
The British submarines drove the Argentinian surface ships (including their carrier) into port.
The RN of the time was as good as any at anti-submarine warfare and had quite modern air defences. I think the Falklands war showed how effective air-launched missiles and submarines were (are).