Hehe. Well you could call such an actor the government - I don't want to quibble on words since I don't like verbal disputes - but there would certainly be many things that differentiated it from a normal government.
Note that getting currency monopoly would give you two sorts of seignorage. Firstly, you would get seignorage on the way there. People would buy your currency using other currencies, which would give you enormous incomes. At the same time, conventional currencies would lose value, which would mean holders of these currencies would lose immensely. Secondly, once you have monopoly power, printing new money in order to get some small amount of inflation a year (which is seen as desirable according to conventional economic theory) will give you 3,5 % of GDP in seignorage a year according to Kumhof (if I remember correctly).
So certainly this would give you huge incomes, and power. Still, you would not have monopoly on power which is the traditional definition of government, etc.
You would, ultimately, not get paid in other currencies (Monopoly! so other currencies have no value) but in real assets and labor. IE, the issuer would end up owning.. most of the economy in question. The only way that does not get shut down hard is if the currency issuer is de facto the government, regardless of whether they recognize that.
Under Kumhof's scheme, the income substitutes for taxation, so that the percentage of the economy run by the government isn't changed, and should in the long run go down some if I apprehend the system correctly. (No national debt, so no commandeering of resources to pay for that.) It also makes the finance sector of the economy much smaller.
In the last few years we have seen two interesting revolutionary ideas on how to change the monetary system. The first is Bitcoin: the most well-known peer-to-peer currency. It has been wildly debated recently and I won't go into the detail of allegations of use in criminal activities etc (for one thing, I don't know much about it). My interest is rather in the money creation part. The people who run the Bitcoin software are rewarded for their work with new Bitcoins - a process called mining. Now the pace at which new Bitcoins are mined is limited, which means that Bitcoin creation is a zero-sum game: the more one miner contributes to the Bitcoin software, the less Bitcoins other miners get. Unsurprisingly, this has led to an arms race: miners spend nearly as much on running the software as they get back in form of new Bitcoins.
The second idea is the Chicago Plan, which was debated already in the 30's, after the great crash of 1929, but which recently was resurrected by Michael Kumhof (senior economist at IMF, of all places). The central idea of the Chicago Plan is to abolish fractional reserve banking - the system by which private banks in effect create money out of thin air. Instead of lending out most of the depositors' money, banks would effectively have to let them stay in the bank.
Instead money would be created by the central bank/government, a process that would generate a massive seignorage for the government. According to Kumhof, it would also have other beneficial effects, such as killing off the "boom-and-bust"-cycles which he thinks fractional reserve banking are mostly responsible for, and diminishing the wasteful parts of the financial sector.
Kumhof ideas' have not been well received. Overall, it is remarkable how little reform there has been of the financial and monetary system given that the world had a major financial meltdown 2008 (and was close to an even greater one, in my understanding). Governments won't challenge the financial system radically in the near future, that's for sure.
Instead radical reforms can only come from private hands. Let us now compare the two ideas. In the Bitcoin system money is created by private hands, but in wasteful ways, which effectively means that there is very little seignorage. Under the Chicago plan, money is created by the government in much more efficient ways, which leads to a large seignorage. Now my idea is to take the best part of both of these ideas: let a private player - more exactly, an altruistic organization such as CEA - produce the money centrally, Chicago plan-like, and let the seignorage be used for altruistic purposes. (Of course, there would be some costs of running the system, but if the system was sufficiently large, these would be negligible in relation to the seignorage.)
If the altruistic organization that did this had a sufficiently good reputation, chances are greater that people would trust the system. Of course, it would try to stop the currency from being used to launder money, drug trade etc.
Generally, people would be suspicious of private currencies where the central authority collected a seignorage, but if this seignorage was used for charitable and other altruistic purposes (and people really trusted that that would be the case), this would, I hope, be less of a problem.
What do you think? I'd be happy to get comments from people who know more about the Bitcoin system, since I don't really know it (though I find it interesting). Perhaps there is some info concerning Bitcoins that tells against this proposal; if so, I'd be interested in that.