The value of currency like other things is governed by supply, so destroying some does not damage anything real in the world, just increase the purchasing power of the other dollars in circulation.

The Government taking money and burning it is called "taxation". With fiat currency, the government makes the money, out of nothing, at its discretion. They then collect most of it back in the form of taxes. Keep in mind, the money they're collecting is going into the pile of infinite money, and Inf + 1 = Inf.

Fiscal policy all about adjusting those levers (how much, and where, the government injects money into the economy, and how much, and where, the government extracts it back out) in order to promote the society we want to have.

Burnt money isn't the same as burnt resources. It isn't the same as burning down a factory or a corn field. Since the value of money is relative to how much of it there is, burning one person's money makes everyone else richer.