> To argue that they are somehow not capitalist is somewhat disingenuous isn't it?
There is even a term for this: "laissez faire capitalism".
http://en.wikipedia.org/wiki/Laissez-faire
> Isn't the basis of capitalism itself wholly dependent on the governmental construct called currency?
No, we've used gold for hundreds of years without any government intervention. Fiat money is relatively recent invention.
More recent example: bitcoin, which works as currency without any governments.
> It's hard to imagine anything approximating the modern idea of trade without those functions.
Yes, but these services can be provided through free market. They'll become more cheap and available. Take for example government-run courts: they are slow, inefficient and expensive(which is the reason why patent trolling is viable: in many cases it is cheaper to hand some money to at troll instead of trying to resolve a conflict using government system).
True, such ideas may seem radical to you(No government, won't there be violence and chaos?!). If you want to know how such system will work, take a look at Murray Rothbard's awesome book "For a new liberty: libertarian manifesto" mises.org/rothbard/foranewlb.pdf . There is a chapter "The Public Sector, III: Police, Law, and the Courts", which you'll enjoy.