Not for the Treasury, who issues coins but not bills, but for the Fed. Every bill is a liability on the Federal Reserve’s balance sheet. Destroy the bill, destroy the liability. That the Fed doesn’t know you destroyed it [0] is irrelevant.

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?