The new USD emission is offset by the increase in value that is produced all over the world. When you have more goods to trade you need more coins to exchange for those goods.
The USD, like other traditional currencies, is stabilized by the many trading contracts that are in effect, and by the huge mass of money on the market. If you decide to drop USD by massively buying the currency for, say, one barrel of oil per dollar, other speculators will gladly buy your oil, then turn around and resell it for 60 dollars. There are more dollars in the world, and more speculators, and more demand for oil, than you have oil to complete your scheme. You would succeed only if you have more goods to offer than the mass of dollars in other people's pockets.
BTC has no such backing. Nothing of economic value is traded for it. Any speculator with sufficient supply of US dollars can manipulate the price of BTC by buying it in volume, or by selling. The small and fixed number of BTC on the market makes that easier; concentration of large number of BTC in wallets of early adopters makes this ten times as easy. For example, if I declare an old airplane ticket a currency, I can ask whatever I want for it, and I could trade that ticket with my friends for any number of USD (or any amount of gold.) It's our private choice, and it has no bearing on the rest of the planet. I can choose to "sell" you that ticket for one billion dollars that I give to you. Nobody expends real USD, but the price of that piece of paper "on the market" is now $1B. What does that price signify? Nothing at all.
An independent currency is a good idea in itself. However BTC has so many problems that I don't see it as a good player here.
Fiat currencies used today are created through debt, its fatal flaw. I'm afraid the only exit is hyper-inflation, as all fiat currencies eventually fail and even real currencies are debased to satisfy the needs of the state.
One advantage that cryptocurrency offers is it takes this power out of the hands of the state and puts it in the hands of the individuals.