The value of fiat currencies lies in their ability to pay taxes, and in general the legal structure that surrounds them. The USD would be worthless if you could not at least use it to pay your taxes in the United States.
Your entire theory is predicated on the idea that currencies are valuable simply because they exist. Supply is not sufficient to create value; demand must exist also, and your theory does not make it clear why anyone would demand any particular currency. Why is CAN not used in the United States? Why are Euros not used in Japan? Why would the citizens of the United States almost all use USD, when so many other currencies exist? Why don't people just use monopoly money?
Take the exchanges away, and you take away the demand for Bitcoin. With the exception of a few cryptoanarchists, the demand for Bitcoin is really the demand for secure and anonymous electronic payments. Claiming that Bitcoin can exist in a vacuum is like claiming that Paypal can exist in a vacuum -- in other words, it is delusional, because people are engaging in electronic transactions for the purpose of spending and receiving their nation's currency.