Such forms of money have existed in the past. But the money isn't destroyed, just 'taxed'. It is called a demurrage currency.
en.wikipedia.org/wiki/Demurrage_(currency)
The ancient Egyptians used such a system with grain deposits. The demurrage was used to pay for loss from rats, for the granary guards, etc.
Middle Ages Europe had a system where the local lord would demand everyone turn in their silver coins for new silver coins, minus a 20% 'fee'. This usually happened once every two years or so. The value of older coins not redeemed would automatically lose 20% of their value.
And <PERSON> invented a system of stamp currency that worked very well in the two instances it was tried in a German town and an Austrian one back during the Great Depression. In both cases, you had to buy stamps to keep the value of your script from devaluing over time. The stamps were sold by the organization that issued the script in the first place. 130
Unstamped notes of course were calculated as being worth less.
en.wikipedia.org/wiki/Silvio_Gesell
Today, a local complementary demurrage currency in Bavaria called the Chiemgauer is in use: en.wikipedia.org/wiki/Chiemgauer
And in Canada, there's the Salt Spring Dollar: www.saltspringdollars.com
In all cases, such a currency enjoys high velocity rates. That is, the rate of exchange over time. Higher currency velocity means more trade is going on. People had an incentive to unload the currency...especially before it reduced in value than they do with regular currencies. So, a lot of investment in hard assets happened -- land, artwork, productivity enhancements, etc. People also donated more money for long term projects like the building of the great cathedrals in Europe. Employment levels are generally higher too. And taxes are paid earlier as well.
All of which died down when the kings took control of currency system in collusion with bankers to institute the debt-based currencies we know today or when the Romans did the same to the Egyptians.
For the two towns in Germany/Austria they were a tremendous success. So much so that the central bank of Austria panicked and declared the currency to be illegal in the case of the Austrian town, Wörgl.
reinventingmoney.com/worgl 130