The need to exchange from one coin in order to trade with merchants of another is a cost. This cost must be non-zero even if automated, as it must consume space and/or time. As such one coin is always "better" (higher utility) than two, to the extent that the resulting coin does not become fee bound as implied by the utility threshold.

We can reasonably assume that two distinct monies cannot perpetually have identical utility. Thiers' Law discusses the consequences of better money in the absence of state controls. From this we necessarily conclude that the better of the two monies will eventually replace the other in the absence of state controls. As this occurs utility accrues to the surviving coin in the reverse of the manner detailed in Fragmentation Principle.

This does not imply that new coins cannot be created or exist over a significant amount of time. It implies that there is a market pressure toward a single coin. A better money in one situation may not be a better or even useful money in another.

For example, gold is not a useful money for electronic transfer and bitcoin is not very useful without a network. One money replaces another in the scenarios for which the former is better.