Scott Sumner and Nick Rowe have both identified so-called Cantillon effects of money creation with "fiscal policy." Years ago, Martin Bailey discussed the basics of the inflation tax in 1956, and Dick Wagner at least partly identified the Austrian-type Cantillon effects with seigniorage revenue in a 1980 article.
I think that this approach is very realistic in the context of today's monetary regimes. The typical government runs budget deficits, monopolizes the issue of currency, and appropriates nearly all of the financial benefit from issuing currency. The rate of inflation impacts how much revenue is generated by the currency, and how that impacts other methods of raising revenue, taxation and borrowing with interest bearding debt, or total government spending or else one type of spending or other, involve public finance. My favorite thought experiment of newly-created money earmarked to one type of government purchase--tanks--is a bit artificial.
Much Austrian discussion of the matter, for example, Steve Horwitz's here, is highly abstract. The new money enters the economy in some specific place--not, the government issues new money and spends it on government programs.
Suppose issue of hand-to-hand currency is monopolized by a central bank, but the central bank is entirely independent of the government. Further, suppose the conspiracy theorists are right, and under this institutional framework, the profits earned by the central bank are paid out as dividends to the stockholders.
If this monopoly were entirely unconstrained, then presumably it could just print up currency and pay it out to the stockholders. The framing of government as counterfeiter could be applied. But instead suppose that the central bank is constrained. Not by some limit on the quantity of currency that it can issue, but rather a requirement that the currency maintain its value. This could be enforced by gold, silver, or some foreign currency. However, consider the scenario where the central bank is required to keep inflation on target.
With some redeemability contract, it is clear that the currency issued by the central bank is a form of debt. The central bank can issue all it wants, but it must stand ready to pay it off on demand. The monopoly privilege of the central bank is to be able to borrow at a zero nominal interest rate. It actually makes money from this by lending at a positive interest rate. (At the zero nominal bound, there is no benefit from issuing the currency.)
In my view, the inflation constraint is really no different than the redeemability constraint. If the inflation constraint can be enforced, say by shifting the franchise for issuing currency to another bank, then the central bank is benefiting from borrowing at a zero nominal interest rate and lending at positive interest rates.
Based on the Fischer relationship, the real interest rate at which the central bank can borrow by issuing currency is the negative of the inflation rate. It lends, let us suppose, at the real interest rate. It's profit margin is then the real interest rate plus the inflation rate. Of course, the same analysis can be made in nominal terms. It borrows at zero and lends at the nominal interest rate, and so its profit margin is the real interest rate plus the inflation rate, the nominal interest rate. Since the real demand to hold currency is negatively related to the nominal interest rate, it would be simple to calculate the profit maximizing inflation rate. However, there is no reason why the inflation rate imposed on the central bank as a constraint would maximize its profit. An inflation rate of 2%, 0%, or even some mild deflation that greatly limits the profit from issuing currency would be possible.
The point of outlining this alternative monetary regime is to point out that monetary policy would have no connection with public finance. A higher inflation rate would result in more real income for the owners of the central bank. A lower inflation rate would result in less real income for the owners of the central bank.
Perhaps those who sell luxury items to people owning stock in the central bank would benefit as well. But this has nothing to do with public finance.
I would also note, however, that the stockholders of the central bank are not getting the new money first, and they profit from the inflationary policy even though prices mostly like rise before they spend their dividend payments. Borrowing at a zero nominal interest rate is beneficial even if prices remain at their equilibrium values--even if there is no excess supply of money.