"The flow stops when the currency is transformed into a financial asset and stashed away as a hedge against inflation."
This isn't true. Any transaction in the private sector is between a seller who desires the currency more than s/he does the commodity and a buyer who desires the commodity more than s/he does the currency. When they reach an agreeable price the transaction is completed and the currency used to purchase the commodity becomes the monetary asset of the seller. Purchasing Bitcoins doesn't in any way negate the flow of fiat currency.
Bitcoin isn't a "system" in the same context as the US "monetary system". It is a commodity that is denominated in the currency of our monetary system, the US dollar. Unless Bitcoin holders can figure out how to gain enough acceptance of their commodity without pegging its value to the dollar it will never gain that level of acceptance. Even if it did, the federal government would likely tax it out of existence, or make its capture too expensive (which it almost is already) to be justified.
The Bitcoin fervor is rooted in the right wing's distrust of anything "big gubmint" and their general ignorance of how their economic system actually functions. It, considering the cost of mining and the limited acceptance it has, is hardly a solution to the issues of poverty and income inequality that it purports to be. It has remarkable similarities to the Hunt Bros manufactured run on silver that almost brought down many financial institutions.