Exactly, that is the alternative system which was the default. It has gone through a number of cycles in history and is not always thought of the same way across different cultures (which is why there is a whole book on the topic).

But it is a recurring theme in history, and most (all?) monetary systems were traded for this alternative within 1000 years. For me, in Western Europe, this was 500 years ago between roughly 1000-1500. The churches were fitted with gold roofs, and because of the lack of coinage and currency, most people lived their lives with this alternative approach, only rarely coming across money, currency, accounting and debt.