Maybe it isn't the return of Monetarism. Or rather, it isn't the return of only Monetarism. Maybe it's the return of Monetarism vs. Keynesianism, 1960's style, applied to unorthodox monetary policy.
At the risk (or certainty) of caricature, the 1960's argument went something like this:
The Monetarists argued that it didn't matter (much) what the government and central bank bought; what mattered was how they paid for it, and whether it was financed with money. Money-financed tax cuts, money-financed increases in government expenditures, open-market purchases of bonds with money, were all essentially the same. Just different ways of increasing the stock of money. You might as well (theoretically) throw the money out of a helicopter.
The Keynesians replied that it did matter what the government and central bank bought; and it mattered less whether they paid for it with money or bonds.
Apply that same distinction to unorthodox monetary policy today.
A monetarist would argue that if you cannot increase the money supply by cutting the overnight rate, because it's already at zero, then find some other way to increase the money supply. Buy short bonds, buy long bonds, buy commercial bonds, buy stocks, buy real assets, buy goods and services, buy tax cuts, buy whatever; or just give the money away. But just make sure the money supply increases and stays increased. It has to be a permanent increase in the stock of money. Fiscal deficits (if money-financed) are just one of many devices to get the stock of money to increase.
A Keynesian would reply that it does matter what you buy. Buying short-term government bonds won't help at all, because they are perfect substitutes for money. Buying long bonds, or commercial bonds, or stocks, might help, because it would reduce the supplies of those assets on the market and might raise their prices. And fiscal deficits will help whether money- or bond-financed.
It also sounds very much like Willem Buiter's distinction between quantitative and qualitative easing. Quantitative easing means expanding the size of the central bank's balance sheet, and if its only liability is money, that means increasing the supply of money. Qualitative easing means changing the mix of assets on the balance sheet, so it depends on what the central bank buys. Monetarists look at quantitative easing; Keynesians look at qualitative easing.
And remember the old debates about the transmission mechanism? Again at the risk (certainty) of caricature:
Keynesians argued that the transmission mechanism from money to inflation went via the short rate of interest, which influenced other rates of interest, which influenced demand for goods. So if the short rate of interest is already at zero, the monetary transmission mechanism is broken at the first link in the sequential chain.
And monetarists argued that there were multiple parallel links from money to demand. An excess supply of money would spill over into the short-term bond market, but also into the long-term bond market, and the commercial bond market, and the stock market, and the supermarket. So losing just one link would not break the net of links between money and the economy.
And this debate does not even make sense in a model of frictionless Walrasian markets, where "liquidity" is an unintelligible concept.
If you believe that this crisis, at least in part, is a crisis of liquidity, and people are desperate for liquidity, then the monetarist position has an at least prime facie plausibility. Liquidity is the ease with which a good can be converted into other goods. In a monetary exchange economy, all goods are converted into other goods via the medium of exchange. Money by definition is the most liquid of all goods, since it is the medium of exchange. So increase the supply of liquidity by increasing the supply of money.
But then buying stocks or commercial paper with money ought to satisfy both sides, and might be the most prudent option, since we (or at least I) don't know which side is right.