The cost of annexation in a hypothetical Anglo-Argentine war

Would Britain annex Argentina after defeating it in a hypothetical 1930s Falklands war?

Annexation is considered too expensive; Britain would more likely seek a different Argentine government.

Adding Argentina to the empire would bring a large expense, making regime change the more likely British objective in this scenario. Existing British contacts in Argentina could help that effort. A replacement government might then join the Allies early in the Second World War. Another rebellion and a turn toward the Axis are also considered possible, which would risk a further war with Britain.