Of course, that has nothing to do with quality of life. That's a different topic. But the point is, the EU and China have nothing in common economically. China is up and coming. The EU is slowly descending into third-world status. By the next foreign incident, the EU will be degraded from "Chattering class" down to "What are they whining about now?" class.
I doubt that. Europe may never reach the top in terms of per capita GDP, but it is a peaceful, politically stable and well educated region. While there is little doubt that we are going to fall back economically, third-world status would mean a struggle for the very survival. Sorry, I simply can't imagine how that could possibly happen.
By the way, I don't get that accusation of us being "whiney". I don't define my quality of life by how much stuff I have, and if the Americans are richer, well, good for you.
Secondly, military power by 2100 will be measured more so in technological might. The army of the 22nd century will be drone-centric. That is, remote controlled robotic warriors on the ground and in the air. It's extremely unlikely that China will be able to take the lead technologically by the 22nd century if ever.
As for Taiwan's fate, by that rationale, the US should have conquered the rest of North America by now since the US could easily done so by now.
China taking the technological lead is a long shot, agreed. But their industrial power is going to develop to such a level that the US won't be able to be confident about a conflict with China forever.
The USA could indeed conquer the rest of North America. They just don't because they live in peace and on good relations with Canada and Mexico, and the American people thankfully have changed their attitude of which land is rightfully theirs since the 19th century (see fate of the Native Americans and the US-Mexican War). The difference is that China believes it has a historical claim to Taiwan, and once they think they can get it at a reasonable cost, I suspect they will go for it.
Another thing: China actually doesn't need to match the military might of the US to successfully invade Taiwan. It just needs a creditable nuclear deterrence (with Russian assistance), the element of surprise, and a somewhat stronger navy than now. The Russian supersonic cruise missiles are a significant threat to American carrier groups, and Taiwan is on China's doorstep, but a long way from the USA. I believe that if China wanted Taiwan badly enough, they could conquer it even today, they are just afraid that the political fallout would hurt their country much more than the reunion would be worth.