Ancient Egypt had two forms of money: one was gold and silver, and the other was grain.

Wheat would be grown by the people, then they'd deposit it in the store house and get a receipt for it. They would then take those receipts and use them as money in the market place to buy whatever they needed such as food, clothing, tools, etc. These receipts would depreciate in value because the grain had a shelf life due to spoilage, rats, and priests who would eat it in return for running the whole system. It's a direct analogy to the proposal in the OP. This type of money system wasn't inflationary, rather it was a flexible system that allowed anyone in society to create money themselves without fighting it out of the hands of rich people. It was a currency for the benefit of society.

On the other side of things, there was gold and silver. This wasn't traded in the marketplace, but rather used as a store of wealth and exchanged for things like land, homes, it was taken on journeys, and used entirely differently than the first type of money. Both of these systems coexisted and were used by people for different purposes.

If you were raising a family, you probably relied mostly on the wheat system because with each person born in the family, gold would be diluted. With the wheat system, there was a constant source of money that automatically adjusted itself based on the population. Decaying coins are slightly different in that they won't become more numerous, but they will have the effect of not concentrating money in the hands of the old, with the young being at a disadvantage. This is important for currency to do it's job. On the other hand, if you desire to store your wealth, something like gold is a lot more appropriate, and it doesn't restrict currency from flowing around in the economy.

Therefore, what we really need is a dual system. Those who want to store wealth for the long term can fight over the limited supply of the first type of money, and those who just want to buy stuff can use the other form. For example, lets say you get your paycheck. You put 75% of your paycheck in the decaying money because it's cheaper and easier to get and you're going to be spending it anyways. The other 25% of your check you put into the scarce money for long-term savings.