> Bitcoin has no similar intrinsic value that isn't easily copied (and possibly improved upon) by any number of altcoins.
What you are calling "intrinsic value" is more correctly "utility value", the value we put on things for their usefulness. However, it is not an intrinsic property of an object. A gallon of water in the desert when you are thirsty is worth much more than a gallon of water to take a shower at home, when you have it supplied by a water utility at low cost. Both gallons are useful, and people are willing to pay for them, but different amounts.
In the case of bitcoin, it is the Bitcoin Network which gives it usefulness. Without the network, you cannot make transactions, and thus any coins you have are useless (you can't send them to anyone, and thus can't buy anything with them). Bitcoin has by far the largest network of it's kind. It consists not just of the relay nodes that forward transactions, but custom hardware, software applications, merchants who accept it, and users. That network isn't easily copied, it has to grow over time.
With the network, I can pay a programmer in Kiev from Atlanta easily, cheaply, and quickly. That's a pretty useful thing. I can also make payment contingent on a software script written into the transaction, because bitcoin was designed with a scripting language. I cam make my money programmable. That's a whole new useful feature.
Like many other networks, bitcoin responds to Metcalfe's Law. The more people who use it, the more valuable the network becomes. This is also true of fiat currency networks. Lots and lots of people use the US dollar. The dollar is thus highly useful, because you can spend it on lots of things in lots of places. Try spending a Zimbabwean Dollar anywhere, even in Zimbabwe. It experienced 10^25 inflation, and now nobody wants it. So if you have a stack of them, they are useless, except as a collector's item. Even though they were issued by a government, the size of the network that uses the currency trumps that.