> But... knowing that they are not underwritten or backed, surely they're only "worth" what somebody will pay for them.
I don't understand how this is any different from a fiat currency. The value of bitcoins are currently being quantified by its exchange rate in USD. Sure, someone could buy all BTC and drive its exchange rate (and thus its value) down. Someone could also print more USD which would create a mass inflation and the exchange rate would be driven up. The exchange rate of all currencies would all be driven up, and the value of USD would go down.
I don't understand how this is any different from a fiat currency. The value of bitcoins are currently being quantified by its exchange rate in USD. Sure, someone could buy all BTC and drive its exchange rate (and thus its value) down. Someone could also print more USD which would create a mass inflation and the exchange rate would be driven up. The exchange rate of all currencies would all be driven up, and the value of USD would go down.