I don't know if it's funny, or annoying, the way people keep forgetting that when you exchange currency, such as Bitcoin into USD, or USD into whatever currency is being proposed here, the currency being exchanged doesn't just disappear. When you quickly exchange out of BTC into USD to avoid currency fluctuations, someone else is buying and holding that BTC, exposing themselves to the fluctuation risk. Likewise, with your proposed idea, when you buy this Bitcoin 2.0 with USD, someone else ends up with your USD. So, basically what you are proposing is gifting a few lucky exchange operators with $21,000,000, totally free of charge, and then making the rest of us give them our hard earned USD for the privilege of using their special freely obtained $21,000,000 worth of BTC.
Even you yourself later point out that "without somebody to take the other side of the trade, your BTC isn't worth anything," so why even propose something like this?
Firstly, it's 21 trillion coin, not 21 million (this market is too small if you're going to peg). Secondly it's pegged to the dollar, on purpose, to avoid volatility. The idea is that if it's pegged, it doesn't fluctuate. All of the exchangers agree to the peg (thru smart property cryptographic mathematical arrangements). The currency doesn't initially float. The net effect is to move as many dollars into many vaults (permanently parked in hundreds of locales) and circulating as bitcoin as much as possible. The exchangers would be the "vaults" for this.
No money disappears anywhere. There is just a transference and preference to bitcoin trading or money away from USD or other fiat.
Initially, people will probably use the coin as a transition between fiat and BTC but without the currency price exposure. Once they realize it's easier to trade in bitcoin, more fiat resides in the vaults (it doesn't move much except to grease the proverbial wheel when necessary). The money velocity demand decreases for USD and increases for bitcoin until eventually all transactions are in BTC or other digital coin. Once you exceed the 21 trillion dollar mark (or some other largish dollar amount) you then go to the float scenario. Hopefully by then, volatility will be less of a factor.
Nobody gifts anybody. The miners who authenticate and secure the network get paid a fee to do so. The exchangers are nothing more than a connection to the fiat market. I'm piggybacking, nothing more.