Krugman hasn't been that clear about why he doesn't like bitcoin. Apparently he mostly does not like it because it is favored by Libertarians. He has endorsed the views of Brad Delong (an econ blogger with similar views and style) that a currency needs to be backed by a taxing authority and/or central bank (i.e. a government):
You're not reading very carefully. The argument De Long makes in the excerpt that Krugman endorses is not that "a currency needs to be backed by a taxing authority and/or central bank", it is that, for a commodity (currency or not) to serve as a stable store of value, it must have something providing both a ceiling and floor for its value, and one of those (the floor) is not immediately apparent for bitcoin.
This is very different from your argument about government, as is evidenced by the fact that his two counterexamples of things where the ceiling/floor combination are available and specifically identified are the US dollar (a government-issued currency) and gold (a commodity which is not backed by a taxing authority and/or central bank.)
Actually I think he is right and you are wrong in this case. The section of DeLong's essay that Krugman quotes in his article though is the claim that Bitcoin was designed as a weapon against government central banks and their ability to tax, and to monitor citizen financial transations. The article "Bitcoin is Evil" was written not to ask "does bitcoin work" but "is bitcoin morally bad or good?" And Krugman says "bad" because he believes it would undermine the government's ability to use monetary policy to achieve various goals.
> The section of DeLong's essay that Krugman quotes in his article though is the claim that Bitcoin was designed as a weapon against government central banks and their ability to tax
No, the section of DeLong's writing that Krugman quoted didn't deal with that, it dealt with the ceiling/floor issue I described; this was in the section of Krugman's piece discussing the postivist evaluation of bitcoin's ability to function as a stable store of value.
What you seem to be describing is the excerpt of Charlie Stross's work that Krugman quotes in the shorter bit at the end where Krugman is discussing normative evaluation of bitcoin's purposes.
Charlie Stross and Brad DeLong are two different people, and Krugman cites them for very different purposes. (One about bitcoin's purpose and one about bitcoin's functional properties.)
I've not read everything he's said on bitcoin, but I've never seen him explicitly make that argument. Do you have a link?