If you think about it, while it would be fairly easy for most modern, long-haul aircraft to operate as you describe; prudence dictates that you need to add a bit of fat in your planning.
As you get into the Southern Hemisphere, en route diversions become fewer especially when you start dealing with the diplomatic issues of the Falklands.
When you get to the islands themselves, which airfield do you nominate as your diversion in case of bad weather or if the runway is black?
Would you carry a lot of extra fuel and hold over the airfield, gambling on the weather improving?
If your diversion is on the South American mainland (assuming Argentina is out), then then you are going to need a fair chunk of extra fuel.
To answer your question, your 7000+ miles is now becoming 8000+ Miles when you consider a diversion. Whilst even that would be possible for some aircraft, you have to start questioning whether they could operate that far without a performance / useful load penalty.
Hope that helps.