Steve Waldman has an excellent post about the immorality of stabilizing the price level or inflation rate. However, it is important to emphasize that his argument only applies to using shifts in aggregate demand to offset shifts in aggregate supply. It isn't saying that it is immoral to have a stable trend price level or inflation rate. And, as he emphasizes, there is nothing wrong with avoiding or reversing shifts in the price level or inflation rate due to changes in aggregate demand.
The argument about the undesirability of offsetting aggregate supply shocks was made (with less moral force, I think) by George Selgin in Less Than Zero. While I don't find George's argument for a mild deflationary trend convincing, he did convince me long ago to give up on price level stabilization because of the undesirability of using monetary disequilibrium to reverse the impact of aggregate supply shocks on the price level.
David Eagle has also provided an analysis of the risk sharing implications of price level stabilization.
This is one of the reasons shy Market Monetarists favor nominal GDP targeting rather than price level or inflation targeting.