Next, ARA Santa Fe and ARA San Luis sail to Acension to lay in wait for HMS Hermes and Invincible
Firstly, had the Argentinians attacked the RN on the journey south it would have represented an escalation of the war with all sorts of political as well as military consequences. The TF was certainly prepared to shoot down Argentinian snooper aircraft, like the B707, had they taken offensive action rather than withdrawn when intercepted by Sea Harriers. Subs would have been no different.
It also ignores the availability of 2 squadrons of Sea King HAS.5 (reportedly the best AS helicopter in the world at the time) on board the carriers and the Nimrod MR2 deployed to Ascension. And if needs be I'm sure the RN would have redeployed one of the nuclear boats to deal with such a threat if it was proving beyond the capabilities of the surface escorts and helicopters, which I doubt it would.
Santa Fe was a old US GUPPY conversion of a USN WW2 sub acquired by Argentina in the early 1970s and, AIUI, little upgraded if at all since then. Noisy and easily detectable. Not much of a threat in 1982.
San Luis was a different matter. She was a modern quiet, German built Type 209 and caused the TF helicopters a bit of difficulty in the inshore waters around the Falklands where underwater sound conditions favoured the sub. But in the open ocean of the South Atlantic that plays to the strengths of the RN helicopters and frigates/destroyers and the Nimrod MR2. It was after all what the RN/RAF had been training for in NATO for years in the Atlantic.
en.m.wikipedia.org
You can read about Argentinian sub operations and RN anti sub operations in the Falklands in this book published a couple of years ago.
Amazon product ASIN 1913336395
View: https://www.amazon.co.uk/dp/1913336395/
Again Argentine timing sucked. Their second Type 209 sub, Salta, was in refit at the time of the Falklands War.
You also assume that the British ROE would not change if the circumstances changed. For political reasons Britain wanted to keep the war contained. But it was prepared to look at operations against the Argentinian mainland. Remember the SAS recce group that ended up in Chile after the Sea King carrying them developed a mechanical problem, or the proposed mission, thankfully cancelled at the last minute, for the SAS to raid Argentinian airfields on the mainland using RAF Hercules aircraft (think of the Israeli attack to free the hostages at Entebbe airport, Uganda in 1976).
If the Argentinians change their actions then I have no doubt the UK would react. The unknown question is how.
While the Black Buck Vulcan sorties from Ascension to the Falklands might have seemed unnecessary to some, they did send a powerful message to the Argentinians that the RAF had the capability to strike the mainland. Especially after that Vulcan caused a stir by landing in Rio de Janiero after it broke its refuelling probe while tanking south. Nimrod MR2P aircraft also carried out recce missions along the Argentinian coast while remaining in international airspace.
The best chance the Argentinians had was to delay any invasion by a month or two. Then U.K. would have been faced with the full fury of a SA winter making retaking the islands virtually impossible until much later in the year, by which time U.K. and world public opinion might have been different. But of course that doesn't suit Argentine domestic politics.