There is no "con" to having a 0% inflation for most Americans, especially those living on a fixed income. Even if the Federal Reserve can keep inflation "contained" at exactly 2%, over 10 years that is a decrease in overall purchasing power of 21.9%.
On a fixed income, not looking for a job, and no investments, I agree.
I am not sure where most people fit.
For me, I like some inflation because I do have investments I'd like to see grow for about 7 to 10 years.
After that, I'm with you. 0% would mean my expenses don't increase and I won't be looking for a job so the unemployment rate increase won't affect me too much.
BUT then again, I think we have to consider the population as a whole. While you and I may not be concerned about investment income or a rise in unemployment, it will affect others.
Part of the problem with our nation now is that each person seems to only care about themselves.
Remember the deflationary economy in Japan?
We have to guard against hyper inflation, but a stagnant economy (0% inflation) is more problematic and difficult to recover than slightly increased inflation. Many economists recommend a higher target than 2% (to help guard against a recession).