What's the internet backed by? You could argue ICANN but that's not absolutely necessary to have an internet, and in fact other countries want their own version of that.

You could argue "the infrastructure of a bunch of ISP companies", but then you can argue that about Bitcoin as well. The infrastructure of a bunch of (eventually) more trusted companies built around the currency (like Coinbase, etc), and the computing power of the miners propogating the blockchain, plus the entire ledger being public and independently verifiable, could earn the trust of many (it might not, but it could).

There are obstacles getting in the way of that, though, including it being such a new and different concept that most people can't wrap their heads around it.

I dont agree, its backed by everyone that participates. This is just FUD that is propagated by those with vested interests for preserving the status quo.

A currency policy that is constantly being manipulated and a money supply that is constantly tinkered with(quantitative easing?) is unlikely to keep the trust of many when there are alternatives.

Any currency that has a supply decoupled from the macroeconomy is doomed to failure as a currency, either through deflation or inflation. Deflation results in hording, at which point there is insufficient exchange and another currency replaces it. Inflation results in divestiture, at which point another currency replaces it.

Maintaining a currency requires threading a needle. Only strong governments have ever been successful at it.

Perhaps there is a technological solution, but it's not bitcoin or any of its brethren, because their growth rate is decoupled from the economy.