If Quantitative Easing (QE), why not helicopter money? We know helicopter money is much more effective at stimulating demand. Helicopter money is a form of what economists call money financed fiscal stimulus (MFFS). In their current formulation independent central banks (ICB) rule out MFFS, because the institution that can do the stimulus (the government) is not allowed to cooperate on this with the institution that creates money (the ICB). In a world where governments - through ignorance or design - obsess about deficits when they should not, it turns out that MFFS or helicopter money is all we have left to prevent large negative demand shocks leading to deep and prolonged recessions. So why is it taboo?
One reason why it is taboo among central banks is that they want an asset that they can later sell when the economy recovers. QE gives them that asset, but helicopter money does not. The nightmare (as ever with ICBs) is not the current position of deficient demand, but a potential future of excess inflation that they are unable to control.
Here it is perhaps easiest to talk about monetary policy as putting money into the system when inflation is too low or taking it out when inflation is too high. QE creates money when interest rates are at their Zero Lower Bound (ZLB), but that money can be taken out of the system later if need be by selling the assets that QE buys. Helicopter money also puts money into the system at the ZLB, in a much more effective way than QE, but it cannot be put into reverse by central banks alone. The central bank cannot demand we pay helicopter money back. 
If the government cooperates, this is no problem. The government just ‘recapitalises’ the central bank, by either raising taxes or selling more of its own debt. Economists call this ‘fiscal backing’ for the central bank. In either case, the government is taking money out of the system on the central bank’s behalf. So the nightmare that makes helicopter money taboo is that the government refuses to do this. 
What kind of government would this be? Inflation is rising, and the institution tasked with bringing it back under control makes a request that can be satisfied fairly painlessly by the government issuing some more debt. A government that refuses to do this is saying very publicly that it no longer cares about high inflation: it prefers an environment of low interest rates and high inflation and it is prepared to cripple its central bank to achieve this.
Now imagine a government with these preferences, and now put it in a world where the ICB does not need recapitalising and is selling assets and raising interest rates to do its job. Are we really meant to believe that such a government would ignore its preferences and let the central bank get on with it? Of course it would not - it would take away the central bank’s independence by forcing it to stop raising interest rates.
In other words, a government that would refuse to recapitalise an ICB is also a government that would have no hesitation in ending central bank independence. Holding assets is no protection for an ICB against this government of its nightmares. 
The reason we have independent central banks is not to stop us becoming like Zimbabwe. It is to stop governments taking small risks with inflation for short term political gain. Like the occasion I was told that the Chancellor (at the time) knew full well that interest rates needed to rise now to reduce inflation, but there was no way that would happen until after the party conference. But this kind of government is not the kind that would deliberately sabotage its own central bank by refusing a request for recapitalisation.
Tony Yates writes of helicopter money: “Once government gets a taste for it, how could it resist not helping itself to more?” This is a statement about a government of nightmares that goes on a spending spree using money created by the central bank, and not about real governments in advanced economies. The idea that a perfectly sober government becomes a drunkard the moment it sees its central bank undertaking helicopter money is absurd. If ever we are unlucky enough to have a government that is a drunkard, an ICB with some assets to sell will not be enough to stop it raising inflation.
So this nightmare that makes helicopter money taboo is as unrealistic as most nightmares. The really strange thing is that ICBs have already had to confront this nightmare. It is more than possible that when central banks sell back their QE assets, they will make a loss, and so will be faced with exactly the same problem as with helicopter money.  A central banker knows better than not to worry about something because it might not happen. So the nightmare has already been faced down. It therefore seems doubly strange that the taboo about helicopter money remains.
 It is sometimes suggested that if the central bank runs out of assets, it can create its own, by issuing central bank debt. This would be effective if the nightmare government was unlikely to last, and a new government would later emerge that would recapitalise the bank. However it seems problematic as a solution for a permanently uncooperative government where inflation is too high, because the only way the central bank can pay the interest of the assets it issues is by creating more money. Corsetti and Dedola treat reserves as an alternative to debt issued by governments, but here the idea seems to be to rule out default as an option.
 An independent judiciary could protect an ICB. However it would be equally possible to write into law the duty of a government to ensure an ICB can do its job.
 The Bank of England obtained an almost complete indemnity from the government for QE losses, but other central banks have not (see Willem Buiter here).
 The central bank could just loan the helicopter money. But in practice this amounts to the same thing: a government that will not back its central bank will tell people not to repay the loan.