Sinking a big ship like the Belgrano made a huge impact (no pun intended) both politically and militarily. When the Belgrano went down, the Argentinian leadership realised they had no answer to our submarines and that we could also sink their real pride and joy the Veinticinco de Mayo, which together with the rest of their Navy promptly retreated to Argentinian territorial waters and stayed there for the rest of the conflict.
Not strictly true. Subsequent British successes proves that they operated beyond that date.(eg. Isla de los Estados sunk by HMS Alacrity on 11 May) The San Luis operated until mid-May and attacked British ships twice without success.