The value of BTC is in the currency itself.
How much is a three year old's scrawled drawing with the note "I love you Grandma" worth? To most people it is worthless, but to the recipient it has worth. Its utility and use value to the recipient is not measurable. The utility and use value of any commodity is not measurable. The drawing has a use value even if no one wants to buy it - it is useful to the recipient.
Commodity values also reflect the work put into them. Let's say I assemble PCs. I buy $600 worth of parts - motherboard, disk drive etc. I spend an hour assembling the parts into a PC. I now want to sell it for more than $600 since I want to be paid for my time, maybe $50 for the hour - it is now $650 total. Each of the components of the PC I paid $600 for the parts of is more expensive because of the labor costs associated with assembling that component. So the value of a commodity is also connected to its labor costs.
Utility can not be measured as it is subjective - like the child's painting. Exchange value can be measured though. I can buy an OK pair of headphones for $20, I can buy dinner for $20 as well. So a certain pair of headphones are worth the same as 20 dollars are worth the same as a certain dinner at a certain restaurant.
We have had currency for thousands of years. Currencies have always held value due to their inherit value as a commodity, not due to being an exchange medium. Attempts have been made over the centuries to try to change this, but it has never been long lasting. The US dollar was backed by gold until 1971. Now paper currency has value due to the US government accepting it for taxes, stamps and so forth, but such things have been relatively short-lived through history so far. Paper currencies like Confederate dollars, Reichmarks in 1945 and such depend on political factors for their worth( http://www.moneymuseum.com/moneymuseum/library/texts/text.js... )
. Gold and other precious metals have retained value over thousands of years, no matter which way the political winds blew.