It has been proposed that the existence of an international non-political (i.e. objective) "value index" will result in people compelling states to "value target" their monies against the index, thereby eliminating price inflation. It has also been suggested that Bitcoin is such an index and will precipitate this scenario.

The leverage envisioned is the option to leave certain state monies for others. The movement is from monies of higher inflation to lower, based on comparison with the index. The consequence is that states must increasingly target their individual rates of price inflation to the index. This result is state monies "asymptotically" approaching the condition of Ideal Money represented by the index.

Ideal Money is state money with a zero rate of price inflation:

...there is no ideal rate of inflation that should be selected and chosen as the target but rather that the ideal concept would necessarily be that of a zero rate for what is called inflation.

John F. Nash Jr.: Ideal Money and Asymptotically Ideal Money

Expression of the theory is both varied and limited (proof is left to the reader). However the above summary expresses all essential elements. Given these limitations it can be helpful to start with generous assumptions. Let us assume that a money can express objective value (see subjective theory of value), that Bitcoin is such a money, and that people generally have the ability to compare the value of Bitcoin to other major state monies. Let us also assume that, despite the apparent contradiction, people will both generally use Bitcoin in trade (the source of the index) and will prefer to use state monies (a necessary premise).

If we also assume that people are free from legal tender laws, and their use of competing currencies does succeed in compelling states to "value target" Bitcoin, seigniorage will be eliminated. However, as shown in Stability Property, the purpose of state money (fiat) is to collect seigniorage, which is a tax. In other words, Ideal Money is a tax collection system that collects no tax. Granting the above assumptions, Ideal Money is the obsolescence of state money. The proposal fails to consider the reason that fiat exists in the first place.

Reconsider now the assumptions. Fiat requires the existence of legal tender laws and as such Gresham's Law (first penned by Nicole Oresme in De origine, natura, jure et mutationibus monetarum c. 1360) always governs fiat:

These examples show that, in the absence of effective legal tender laws, Gresham's Law works in reverse. If given the choice of what money to accept, people will transact with money they believe to be of highest long-term value. However, if not given the choice, and required to accept all money, good and bad, they will tend to keep the money of greater perceived value in their possession, and pass on the bad money to someone else. In short, in the absence of legal tender laws, the seller will not accept anything but money of certain value (good money), while the existence of legal tender laws will cause the buyer to offer only money with the lowest commodity value (bad money) as the creditor must accept such money at face value.

Wikipedia: Gresham’s Law

The proposal incorrectly assumes that Thiers' Law governs. If this was the case people would not use fiat. It also ignores the existence of foreign exchange controls, which exist specifically to prevent capital flight. Such controls strengthen as capital flight accelerates, in order to preserve tax revenue. Finally, such controls materially limit price discovery in the index, making it less useful than the envisioned reference.

The proposal offers no rational explanation for how people will become able to move between state monies in the face of such controls. It assumes that people will better recognize the tax, due to the presence of the index and their ability to compare against it, and therefore will more effectively control the state's appetite for the tax. Given the near universal use of gold as a comparably objective index prior to the evolution of global fiat, it is not clear how fiat ever took hold if we can assume people will react to it in this manner.

There is an argument that Bitcoin is an objective index whereas gold is not. This is based on the inflationary supply of gold in contrast to the fixed supply of Bitcoin. This assumes that monetary inflation implies an unstable money whereas fixed supply implies a stable money. As shown in Stability Property, both monies are stable. The argument fails to acknowledge that value, as indicated by the index, is a consequence of both supply and demand. Gold demand is stabilized by inflation and Bitcoin's demand is stabilized by fees.

The theory is therefore invalid. Either fiat will cease to exist or it will collect tax. States only surrender this tax under extreme duress and in such cases only briefly. If anything the "ideal money" will be Bitcoin, and it will not trade freely with state monies (to the extent they remain).