...If they just destroy those bonds, then government will get 40 billion dollar free money to spend each month. I don't see any problem with this. ...
Umm... There will be massive inflation. It's a zero sum game. You don't *really* think that printing more paper bills actually generates more wealth (ie, better living standards) for humanity, do you? You just get more money chasing the same goods/services, so people start to competitively bid up prices for things and the overall price level rises. In theory, that has no effect on anything; people would make more money and spend exactly the same amount more money. In practice, it triggers massive friction in the form of ever rising prices (because people fear prices for goods they buy will rise, thus they preemptively raise the prices of the goods they sell, etc...), to the point where it's difficult for business to function because the price level is moving too fast.
Because of money's universal equivalence property, money itself IS wealth. Are you sure that when you lost money, you did not lose any wealth? Economy books always say that money is not wealth, but how come the wealth was destroyed in financial crisis while none of the houses/cars/goods/services were destroyed?
And there is cantillon effect, those who first receive the newly created money have to spend it to cause inflation. If he carefully select his spending target (or even move them oversea), the real inflation on the end of the chain might take years to happen, or not happen at all. The result is that more and more money accumulated at the top of the chain, creating huge gap between rich people and poor people
Well, I parenthetically defined "wealth" as better living standards, not money. But I don't want to get into an argument of definitions; what was destroyed during the crises was unused purchasing-power that could not last. Nominal levels were too high, and too few people were converting paper balances to real assets to make that obvious until everyone did simultaneously. Classic.
In any event, I think I see the root of your issue. Essentially, you think a small group of people can successfully plan an entire economy, benevolently taking into account all the complexity of human desires and actions that that necessarily entails. From an academic perspective, I agree that it should be possible to control the money supply such that ideal low-friction conditions are achieved, and targeted expansions/contractions of the money supply should be able to provide short-term nudges in the "right" direction for the business-cycle, etc...
The problem is that humanity doesn't work that way. Economies are incredibly complex, and it's downright arrogant to think that a small group of people can distill all the variables, with all their error curves and varying relevance, into sensible action. Human economy is a complex chaotic system, in the true mathematical sense of the term. Small inputs can lead to huge and unpredictable results. What you will inevitably get if you try to directly manage it is a small group having an increasingly outsized influence on the economy as a whole, and having to use ever increasing measures to get their desired effects, until one day, it just doesn't work anymore and the whole thing fails.
I agree that the math for controlling the money supply looks nice. I just think it's awfully arrogant for someone to think that they're smart enough to successfully shoe-horn the myriad and unknowable complexities of humanity into that model.