Destroying money would cause an unfair loss of purchasing power to whomever had possession of the money. A more amicable solution would be to stop producing new bills. This would decrease the amount of money in circulation by not replacing bills as they leave circulation. This would strengthen the value of the bill.
Economics 101: Trade is good. If you tried building all the things you own your self, you would have no free time, and a pretty horrible quality of life. So that is why we figured out that if we specialize in a few goods and services, and trade those things for other goods and services. There is nothing cut throat about me trading my cow for your farm tools, or your Pokemon card for my bubble gum. Money simply makes those transactions easier, safer, and faster. If we got rid of money, we would still have wars, much more poverty because of inefficiency, and no real way to retire or save money because removing money just slows down the necessary trades and payments of life.