> The USA must defend Taiwan even at the risk of nuclear war.
I don't think this is a popular or maintstream position, nor does the rest of your argument support it.
>The dollars position in the world allows the USA to run its current accounting.
I am not sure what this means. Every nation has a current account. Accounting is just how we track what that account is. Nothing allows accounting to happen, we just do it.
The U.S. is uniquely generous (or from an alternate point of view, uniquely foolish) in allowing the rest of the world to purchase unlimited dollar denominated assets. This makes the U.S. the safe haven for everyone that needs to park export earnings, and thus incentivizes the rest of the world to run huge surplus against the U.S. This is what is meant by "the dollar system". If tomorrow, the European Union would allow unlimited foreign purchases of Euro assets, and provided what is believed to be rule of law and respect for foreign investor rights, then the rest of the world would gladly diversify away from the dollar and the dollar system would end. That was the original vision of the Euro, but the moment there is any crisis, the EMU reveals that it doesn't have the same level of openness for global investment as the U.S., and that dream is proved illusory. So the global dollar system continues, and is in no way dependent on Taiwan or any other exporter. You get to be a reserve currency by importing the most, not by exporting the most.
> Allowing China to take Taiwan destroys the economy and the position of the USA in the world.
It does not affect the economy of the U.S. in either direction, except that the resulting chaos would be bad for markets. Having one foreign export power taken over by another is a null op when determining where can the rest of the world park their money. Of course we may block China from doing it, and that could escalate into a war, which would be disastrous for two nuclear powers, but there are easier ways to punish China -- e.g. seize all their foreign reserve holdings (which are held in custodial accounts in various foreign central banks), block all trade, stop the shipment of any oil. For a nation dependent on exports and dependent on foreign nations allowing China to hold large accounts in their financial system, China is tightly integrated into the global system and uniquely dependent on the good graces of that system. They would have been better off taking physical delivery of silver as in the past.
Not a single bullet needs to be fired to cripple China and destroy its economy. It would also seriously damage the global economy and spread hurt around the world, but this type of economic warfare is better than nuclear war. Whether Taiwan is worth it is a completely different question. But in such a battle, the dollar becomes even more important, not less, as it would be the global safe haven currency (for everyone except China).