When inflation expectations are well-anchored, the occurrence of an adverse aggregate supply shock does not necessarily mean that the central bank must raise interest rates aggressively in order to keep inflation under control, and hence the commitment to price stability can help avoid imposing unnecessary harm on the economy and on the workers who are most vulnerable to a weakening of economic activity.
Now that we see the benefits of maintaining a commitment to a nominal anchor, one might naturally think that there would also be benefits to establishing a similar sort of anchor for the maximum level of employment. But that thought would be incorrect.