But if all central banks ease similarly at around the same time, there is no exchange rate channel: we trade with one another, not with Mars. There are, of course other transmission mechanisms, but once we cancel out the exchange rate channel, the overall effect for any one economy is reduced.
First, because some firms face costs in changing their prices, a rise in the general price level tends to generate undesirable movements in relative prices, thereby leading to an inefficient allocation of resources. This relative price dispersion increases with inflation, and the desirability of minimizing these relative price distortions provides a key rationale for price stability.