But after the initial exchange, another random element is generated: the bill is torn in half, so if you want to forge your part, you'll have to tear it in just the right way to match the other part. This is probably going to be even more difficult than forging dollar bills in the first place.
A gift in the amount of $1 divided by the total number of dollars.
The parent is wrong that it's a gift of $1 to the Treasury.
It is a gift to the government however, as you note in your own explanation. It just increased the government's USD purchasing power. The US Government is an epic scale spender of USD (millions of employees, $4.x trillion budget).
The government does not possess all wealth.
It also issues a lot of USD-denominated debt; deflating the dollar makes that worse.
If the government's dollar liabilities exceed its dollar assets, the impact of destroying a dollar on the government's financial health is negative.
If you destroyed a coin that would be a “gift” to the Treasury, except the metal and cost of production to replace the coin might be larger than the worth of the coin (I.e. you destroy an old copper cent)
[0] dollar bills circulate like mad and are accounted for every time a bank gets a hold of them (often, due to vending machines, strippers, and diner waitresses). If a bill stops showing up, you can assign a high degree of probability that it will never show up again. Every one bill is probably long tailed, but money is fungible, so who cares if any one bill ends up re-appearing?
> Destroy the bill, destroy the liability
Except it is illegal to randomly destroy a banknote (coins are different).
We're talking about drug dealers and other major crime perpetrators... And you're thinking they care about the crime of 'destroying a bank note'?
I think it'd be safe to chalk that up to "I don't think they care".