The reason it has value is because people have demand for it. People have demand for it for a variety of reasons. I think it's reasonable to presume that a non-trivial portion of that demand is driven by the features that make it a rather good black market currency. It's also obviously quite appealing to certain groups of privacy conscious individuals. I've heard it's somewhat popular for international remittances, which makes sense given the economic stability issues various places have around the world. On top of those fundamentals, demand is further inflated by speculators.
Your biggest criticism seems to be that it would be a bad national currency because you can't implement a bitcoin monetary policy. But none of the demand for bitcoin is driven by that factor, so the observation is simply irrelevant.