You can't simultaneously support British balkanization and think the UK should have an imperialist outpost in South America lmao. There's a reason why the Global South as a whole supports Argentina's claims to the Malvinas no matter how many times Anglos, including the ones here, cry about "the Falklanders' sovereignty." How very convenient these Falklanders aren't asking to be their own sovereign country but part of the UK where the UK has access to its oil and territorial waters. They couldn't even ask to be a Commonwealth state like Jamaica. At least Taiwanese, Uighur, and Tibetan separatists have the decency to pretend their respective republics would be an independent country and not just some US proxy state when the Falklanders couldn't even do that.
I do kind of think Taiwan is basically a settled issue. There was a war 70 years ago and it resulted in this split. Yes the people there would be better off if the PRC had control of the island but no one would be better off if they started fighting back up again. It isn't a pressing issue though
China has a legal and moral claim on Taiwan but making an issue of it would just be bad for everyone involved
Ultimately this is why I flip flop on it. In terms of popular support though people will always side with "What do the people living there want?" and this is what makes it a mess.
I think part of the reason support for being part of Britain is so high is the implicit threat that without British protection then Argentina would take the island and they'd be shit out of luck, potentially even kicked out. Taiwanese separatists are similarly reliant on American protection and the majority of Taiwan wants to "maintain the status quo" because they know what it means if the status quo changes. Similar story there in my opinion.
With all that said, Britain losing more would be good. If the islanders can have their security and existing laws guaranteed then changing hands of the island is probably fine.
There's so many things that the UK (and Argentina) could've done if they actually cared about the people living in the Falkland Islands/Malvinas instead of using them as geopolitical pawns. Like, if we must insist that the Malvinas get labeled "Falkland Islands (UK)" on maps:
The UK could de jure or de facto cede territorial waters to Argentina.
The UK could demilitarize the island.
The UK could grant Argentina fishing and drilling rights on the islands.
The UK could offer to pay a lease for the islands.
The UK could buy the islands from Argentina.
The UK could offer a trade agreement favorable to Argentina for the islands.
The UK could have a similar arrangement like the PRC and Portugal regarding Macau where the island belongs to the UK but is administered by Argentina (or vice versa).
Nobody on the islands has to get deported to the UK and both countries can save face. But the UK had absolutely no intentions for diplomacy.
It's "4000 shepherds on a rock" who give the United Kingdom territory in South America, if it was "just 4000 shepherds" they would be fine without the UK's military presence in the region.