I think you're missing the whole "wealth creation" thing. It's not only about money. It's about wealth. The government can't create wealth, only spend more and more. That's why they need us, private sector, to take the money and multiply the correspondent wealth.
Discussion
It strikes me that a large public sector is a means to channel fiat into circulation, by paying the only people left with proper terms of employment - public servants - enough that they can leak it out to others by personal spending. Another approach would be small government, pay private sector for essential services only leaving the rest up to individuals, bid for the best deals throwing it out to competition, and appoint treasury to control how the rest flows out to the population through retail banks cutting out central banks altogether.