I will come back to this in a minute. Ultimately, the risk of contagion between countries was also underestimated when monetary union was established. In response to the crisis, rescue mechanisms such as the EFSF and ESM were put in place, and they did manage to contain the fallout somewhat.
For a country with large percentage of population still living below the poverty line, inflation works as a regressive tax. Economic welfare of the population at large could be enhanced primarily through higher growth, that too in a low and stable inflation environment. That suggests why balancing growth and inflation becomes so important to monetary policy.