So now the bar has shifted from being able to defeat the enemy to being able to defeat the enemy so fast it won't be able to do anything. That's not gonna work on the budget.
Even back when British Empire was a premier military power, people did invade British territories and British had to concentrate forces before taking them back. You can't be overwhelmingly strong everywhere all the time.
Not a goal post shift.
A power of Britain's level even post Empire should have been able to make sure that Argentina never got as far as they did. It all ties into the main point I have been making and having a small military is fine but you have to accept the downsides.
By the late 70s Britain was down to a minimal navy and looking at more cuts. They had plans for sell off ships, only had escort carriers that could fly Harriers and many ships stuck in dock needing parts and repairs. It was a popular move to cut the military and shift spending else where after all NATO(Amercia) would be there to handle the heavy lifting. Like you said the Empire was gone and they had a moat with Western Eourpe as a buffer against the USSR.
But imagine if Britain could of had a Carrier Group on station or been able to surge the size of the garrison before the fighting. Argentina would have ran away with out firing a shot or ended running back with their tail between their legs. Even doing simple freedom of navigation exercises would have probably stopped the war before it began.
Britain didn't need to be strong everywhere. No one was going after their holdings in the Caribbean. The only contested holdings Britain has outside of some disgruntled former natives without power are the Falklands and Gibraltar. Gibraltar is close enough that even the limited military of of late 70s could have protected it. The only other holdings Britain had at the time that was under threat was the Falklands. They only had to be strong in two places the Home Islands and the Falklands. Everthing else only needed minimal protection at best.
If they want to have the cuts and smaller Navy then Britain has to accept that they will be reliant on Aliies aka America's good will or in for a longer war. Britain strained it self to keep the Falklands because they lacked the ability to launch large scale operations easily on the other side of the world. They where lucky that Argentina was a two bit power. In general Whitehall thought the same as they canceled the decommissioning or sell off of several ships. They stopped planned cuts to the Royal Navy and in general increased maintenance of existing ships. The political situation changed in Britain. The military was no longer an easy target for budget cuts. The public wanted to see their goverment defend Britain even their few far flung holdings.
But the main point is the military for Western Europe is generally seen as unnned expect for defense so it is a popular target in budget cuts and easy to get a PR win for the government. It is a popular move and with large portions of the general public agreeing so the governments keep cutting and not expending money to replace worn out gear.
I am sure that you will see this change if Amercia continues it retreat from the world stage and the Middle East continues to destabilize. If the public lic see a new threat to themselves or it effect their daily lifes then cutting the military will be a death sentence for Politicians.