I'm talking about the ability of governments to restrict the activity of citizens and also to fund themselves from said activity.
Bankers hate BTC because it removes them as intermediaries between people and their money, statists hate it because it ruins their socialist dreams of generating funds on demand (printing money) and makes inflation virtually impossible to them.
Fiat currency would fall by the wayside in the most real sense, and that scares the hell out of them (or it will).
As snikto and enki discussed below (great explain guys!) : "using up resources is not valuable by itself. forcing someone to spend on anything, anything at all, does not lead to a good allocation of resources. it might increase GDP, but it does not create value"
I would even say that such a misallocation of resources has a cost - the opportunity cost of the alternative, the proper allocation of resources.
Nation-states existed in Europe before WW2. They may or may not always exist in the future, but now we have something new: countries which borders do not match the ethnic boundaries- the advantage is that citizens are not so strongly bound to a national identity, and thus can start pitting countries against each others.
There is competition between countries for skills. If you are talented and not lucky to have been born in a rich country, you can decide whether to immigrate to Canada, Australia, Germany (etc.) - this is a market.
If you have a european passport, with Shengen rules you freely decided where you are doing to work. Just look at where the talented greeks and spaniards go.
The island scenarios is more like offering people the choice between a german-run island or a greek-run island, each voting with their feet. Sure there still is a cost of having a government, but it's going down, and will go down as fast as new choices are offered.
Identification to nation-states was a limiting factor in the past, but there also seemed seemed to be some kind of network effect where it was harder to be a small country, as it there was some kind of cost (the higher risk of being invaded?)
Now look at Luxembourg and Singapore - it seems than being smaller is no longer a disadvantage.
Something is changing.
The federalism of the United States is a play to push power to a more state-sized scale (taxation, education) while still allowing for powers at a larger scale that need to be there (civil rights, defense, EPA).
Anarchism isn't really about abolishing power structures, it's about pushing more things down into even smaller structures (cults of personality, architectures, local cultural practices, etc).
The idea behind what your OP is saying isn't that nation-states will go away, it's that many of their current roles will be pushed off into larger, global structures whose "muscle" is not military, but cryptographic.