OT: All-Out in the Falklands

[Webstral]

I read a piece about the Falklands War recently. I started thinking. What if the Argentines had gone all-in in 1982? After the initial naval encounter in which HMS Conqueror (I think) sank an Argentine destroyer, the Argentines backed off and let the Royal Navy control the waters around the Falklands, albeit under air attack. What if the Argentines had gone all-in and had initiated a winner-take-all naval battle for control over the sea around the Falkland Islands? I don’t a very good read on this, not being a naval man. Opinions? Preferably with some substance?