For example, a ubiquitous implication of monetary models is that a Friedman rule is optimal. The Friedman rule (that's not the constant money growth rule - this comes from Friedman's "Optimum Quantity of Money") dictates that monetary policy be conducted so that the nominal interest rate is always zero.As I explained before, since most money bears interest, this is instead an argument about the optimum currency-deposit ratio, not the optimum quantity of money. Further, I believe that the cost of transforming real investment projects that take time into money that can be spend on time involves real risk that cannot be avoided. Treating the trivial cost of printing currency (or the lower cost of data entry for deposits) as the cost of creating money is an illusion.
What does this tell us about "monetary models" that have this ubiquitous implication? Maybe the models are so abstract and simplistic that they exaggerate trivial elements of the monetary order. Maybe if there were a one good economy and so a single money price, and hand-to-hand currency as the only store of wealth, then making sure that one price falls at the real rate of interest would maximize utility.
On the other hand, in a many good economy, where firms buy inputs to produce outputs, so that there are both many output prices and many input prices, where nearly all money pays nominal interest, where there are many debt and equity financial assets that serve as stores of wealth for households, and where saving and investment appears to enhance labor productivity as well as allow savers to transfer consumption into the future, maybe, just maybe, making sure that there is a deflation so that the currency portion of money pays the equilibrium real interest rate is a trivial matter.
In a multi-good and resource world, prices have a key role in coordinating the allocation of resources and the composition of demand. In a one good economy, all that the one price must do is maintain monetary equilibrium. The market for the one good is the market for money and vice versa. The essential quality of the medium of exchange, that it trades on all markets and so has no unique market of its own is lost.
Further, in a one good economy, any supply shock is necessarily to that one good and impacts nominal income with real income at a constant price. Why vary the price of the good? The real world issue of a supply shock to one good, rather than simply causing a change in its price, instead requiring changes in the prices of all other goods and resources to stabilize a price index, just doesn't arise.
Similarly, if there is only one good, then any unexpected supply shock shifts real income between creditors and debtors, but the whole point of the contract would be to share that risk in some way. The reality that creditors and debtors create contracts to share risk in one market, say bondholders and stockholders sharing risk in the ice cream market, and then there is some supply shock in some other unrelated market, for example, the oil market, just doesn't arise. If there is only ice cream and it is the only market that can have a supply shock, then changing the quantity of money to keep the price of ice cream constant, and sharing the gains and losses as agreed by creditors and debtors is sensible. However, shifting the quantity of money so that when the price of oil rises, the creditors in the ice cream market are compensated for the reduced ability to buy oil with an increased ability to buy other goods, a compensation that can only come from debtors in markets throughout the economy, makes little sense.
Now, I grant that these real world complications might be difficult to analyse formally. But either we must do without formal models, or it must be done. Models with inter-temporal utility maximization might be nice, but simplifying the economy to a point where the important issues are ignored is like looking for lost keys under the street light because that is where you can see.