The reason that burning money is a bad idea is related to the multiplier effect.
Look at what happens when you spend money. In made up numbers, out of $1000, $100 goes for groceries, $100 for car payments, $50 for gas, $250 for rent, $100 for clothes, $100 for braces for your kids, $100 for tickets to a game, $100 for taxes, $100 into savings. That means that the supermarket can pay its employees, and overhead, and buy more groceries. Your auto dealer can order new cars. The dentist can hire a new dental hygienist. The government can pave the streets. The bank can lend money out to a new business. Spends begets spending. Each type of activity has its own multiplier, but it’s not out of line to say that each dollar spent creates two dollars in total activity over time.
This is great. The more money spent on goods and services and investments and infrastructure, the more jobs are created, the more tax money collected, the more banks can lend out, the more businesses can build new products.
This is also why deflation is hated by all orthodox economists. If you spend less, some purchases don’t get made, some bills are defaulted on, governments collect less money, banks have less to lend out. Everybody suffers. (Technically, deflation does increase the value of a dollar and so makes purchases less expensive, and also benefits creditors because each dollar returned is worth more. But society as a whole suffers because spending and employment drops.)
Burning money is the extreme form of deflation. There is no multiplier effect; money is simply withdrawn from the economy. If enough people did it to noticeably make a difference, the difference would be all bad.
This is all oversimplified, of course, but it’s hard to overstate how important the movement of money across the economy is.