Why Do We Care So Much About Inflation?

Which would you rather have to deal with:

Having to pay 8 dollars more for your average grocery bill a year from now but having a good paying job, or having to pay 3 dollars more for your average grocery bill a year from now but be out of a job?

Mainstream economists, particularly those with a more right-wing bias, have typically preferred the latter to the former.  I've never really understood why.  Textbook economics tells us the costs of high and unstable inflation: including the non-pecuniary costs of more ATM visits, more visits to stores to compare prices, and, in monetary terms, extra travel costs.  Textbooks also speak of concerns of unstable inflation leading to hyper-inflation and unstable inflation leading to mismatched expectations which can redistribute wealth from lenders to borrowers (which might explain why economists and bankers don't like inflation).

But it's never been made clear, to me at least, from an opportunity cost perspective, how these costs are so much more problematic than the costs of under/unemployment.  I've never understood why inflation - a nominal variable - has such a deferential place whereas employment and real output are sacrificed.   It's gotten to the point where pundits raise eyebrows with even slight increases in inflation.  As if somehow that extra 0.2% inflation is going to wreak havoc on our economy compared to the 15% underemployment rate, stagnating wages, etc.   

Luckily some economists are being more vocal in their annoyance at the inflation hawk positions, example: IMF, and the blogosphere:(1) (2).  

More people are calling for the Fed to stop focusing so much tunnel vision toward inflation at expense of the big picture.  At a minimum, the Fed should be required, as the authors of the IMF reports say, to:

... watch many targets, including the composition of output, the behavior of asset prices, and the leverage of different agents

Despite these arguments, the inflation hawks are still winning the war.  

I do think mainstream economics can learn something else besides breaking out of it's obsession with inflation.  I think they can learn from the Modern Monetary Theory crowd that, at the end of the day, the Fed has no real control over inflation.  All one must do to see this fact is observe that the Fed has reduced it's effective rate to 0% from 2008 to the present and pumped reserves into the economy.  Mainstream theory suggests that, via a money multiplier process, this should lead to inflation.  Reality is that there is no such thing as the money multiplier, and that the reserves are just sitting on the balance sheet of the banks.  The real economy isn't seeing those dollars and so there is no real inflation.  The Fed can only control inflation when viewed in tandem with the legislative and executive branches of government regarding taxing and spending policy, or insofar as the private economy changes it's behavior in the face an altered interest rate policy.  Since the Fed has limited control on the legislative process and on the behavior of the private market particularly during financial crises, the Fed has limited/no control over inflation.

I've expressed my skepticism in the past as to the functionality of so-called 'functional finance' so I'm not going to comment further on the reliability of politicians to help our economy, but I will say the big takeaway here should be the Fed should focus on things it has a direct positive impact (like better-regulating the financial sector to prevent bubbles and bursts in the first place) and stop focusing on something which they have little control over (inflation).

IE. Monetarism is dead.

Clarification:
I've been focusing on my view of the Fed's power or lack thereof if response to demand shocks.  I suspect that in fact, when a boom or bust is not demand led but rather supply (commodity) led that in fact the Fed's traditional tools are more effective.  In fact, most of our inflation/deflation have been due to supply shocks and the Fed has had success in correcting them in the past.  I suspect the only reason a traditional Fed tool (rate) is effective in supply shocks is that the Fed can more easily alter the behavior of the private market on aggregate demand when the crisis itself is not a crisis of demand. One might imagine that the reason for the demand shocks (like a financial crisis) means the Fed has little control over mitigating, while a supply shock in an otherwise healthy-demand economy can be mitigated by the Fed.  Textbook economics, as it is taught to million of econ students, meanwhile generally assumes the Fed to be equally powerful no matter the origin of the shock.  I would hope future research breaks through this assumption.