This is certainly key to the appeal to the current enthusiasts, but (to pick an obvious example) suitcases full of dollar bills or Krugerrands are also decentralized and anonymous, compared with centralized and usually non-anonymous methods such as credit card transactions or bank transfers. Most people don't find these other decentralized and mostly anonymous currencies to be especially interesting unless they are engaged in illicit activities or traveling to places where the banking system cannot be relied upon.

I expect the actual appeal is that the value is these attributes in common with the fact that it is virtualized -- i.e. the value resides in data rather than in a physical object such as dollar bills or gold. With data, you don't have something tangible that you have to smuggle across a border in person, you just store it safe somewhere and retrieve it over a secure computer connection wherever you need it.

Or alternatively, you could use bitcoins to purchase something else virtual anonymously. (If you use it to purchase something physical, than there is an audit trail attached to the transference of the physical goods that defeats some if not all of the value of the anonymity.)

Perhaps this makes bitcoins especially useful for some scenarios, but overall I haven't yet seen any use cases that lead me to believe that this is a breakthrough of any particular kind.