The notion that we can't do this, is the one i have problems with because its absurd.
The money a government gives to citizens must come from somewhere. They could liquidate assets owned by the government, borrow it from another government, take it from entities who are subject to the government's authority (taxes), or - what I assume you're getting at - just make more of it.
That last one isn't as simple as it sounds because it doesn't increase the cumulative value of the currency. Printing dollars is like dividing a pizza into more and more slices. It doesn't increase the amount of pizza. Inflation is a very real problem that has annihilated economies.
In any case, value fiat money is not a product of rarity, it is a statement of the value of future tax receipts. Money encodes/is an exchange marker for work done or promises of work to be done.
We could have done a blanket shutdown for 1 month, paid everybody to stay home and it would have cost multiple order magnitudes less than the current nightmare approach, that not only still impacted the economy, also caused 100's of thousands of dead people. This was a preventable catastrophe, caused because corporations are better represented and more important to our politicians than actual citizens. Thanks Citizen's United for legalizing blatant corruptions /s