to answer your question ‘Why are we still in the Falklands?’
Two reasons :
1) we have only been out of the islands for a short period in 1982 other than that we have maintained a military presence there since 1833. 2( the more important answer is that the Islanders want us to stay. As they put it the islands are commonwelth territory and that’s the way they want to stay.
In view of the second answer I’d say who are we to argue?

The answer, as usual, is probably a little deeper than that.

Initially, having won the islands back we saw an opportunity to sell licences to fish. To enforce licences you need a fisheries inspector.

Now, with the new UN rules on the extension of territorial waters based on the continental shelf, there is the potential oil revenue.

Argentina claims that the continental shelf is an extension of the South American mainland and this includes the undersea portions out beyond the Falklands. OTOH, as you might expect, HMG has a contrary view.