Non-monetized economies are more important than monetized economies. When economists or game theorists ignore this, they make mistakes in their analysis of rationality.
A monetized economy is the sum of the transactions where money is exchanged. The money is a simple, quantified representation of an estimate of value. Person r pays $y for thing x, where statistically there is some association between the price y and the value of thing x. This makes it convenient to track estimated value.
The non-monetized economy includes everything from parent-child interactions to having a dinner party to gazing at the starry sky. In all these cases, there is creation of value, but there isn’t as simple a way to quantify an estimate of it. Yet, these non-monetized transactions or activities form the majority of what is valuable in a person’s life.
Consider the Ultimatum Game (see here). Part of the tension in the analysis is resolved once one realizes that the non-monetized payoffs can be much more important than the monetized payoff, and so therefore seemingly irrational behaviour can be rational (and, vice versa, seemingly rational behaviour when only looking at the monetized payoffs becomes quite irrational when looking at both monetized and non-monetized payoffs).
The problem with monetized economics is that it is radically incomplete. When people worry about monetized economics, they are worrying about something that is a part of the overall economy.