A friend of mine once lived in a small Swiss village, in which his favorite restaurant closed during dinner time, so that the waiters and chefs could eat.
In theory one can overcome the problem of coincidence of wants. But it is not possible to overcome the coincidence of time. The dispute is all about the role of time, as money is the link between present and future.
Imagine a small economy in which a baker bakes bread in the morning, sells it to a restaurant, and then in the evening goes to the restaurant to eat dinner. He cannot eat dinner while he is baking (and selling) the bread. And the restaurant cannot buy the bread from the baker while it is serving it to customers. The transactions are necessarily separate by time.
Therefore the baker sells bread to the restaurant on credit, and then extinguish the debt when he eats. When he is selling the bread for an IOU he is saving. When he buys the dinner he is dissaving. But it depends on your perspective; it could be that the restaurant sells a dinner to the baker on credit, saving, and then buys bread the next morning, dissaving. The two operations are equivalent.
More importantly, imagine a farmer taking a loan of seed, planting it, and then producing a harvest. He then repays the debt. In the exchange of a good for a paper claim — both sides are receiving something “real”, except that only one of those goods exists at that point in time, and the other does not yet exist.
To remove this exchange and pretend that only goods are being exchanged for goods, you are removing time. That would require compressing the transaction so that time (and production-in-time) are squeezed out.
The reader is invited to drape a thin blue veil over the computer screen and view the exchanges as real goods for goods.
Here, time has been compressed, but prices are determined at each point in time, not across time. At each point in time, as one farmer is taking out a loan, a different farmer is delivering finished product. Both are exchanging goods for money. Prices will be determined by relative shifts of one over the other at each point in time, not by the personal intertemporal trade-off of each.
When looked at from the point of view of each individual, the transaction is good-now-for-good-later. And that may well be how each individual thinks of the transaction. But that personal view is not what sets aggregate prices or output — those are set by the time slice, in which the exchanges are goods for money, not goods for goods.