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Issuing fiat money profits of course to those issuing it (the state, the central bank, those giving assets to the central bank against fiat money...). By increasing the fiat money stock, this seigniorage is paid for by all those who held fiat money they obtained by working for it, because of the inflation they suffer...
This is the basic misunderstanding of most on this forum--believing that the state is a separate entity, rather than themselves.
The state is not a separate entity, it is the sum total of people of the state. No more a separate entity than the pool that you aim your hashpower at.