What I find kind of surprising is that I thought this was obvious. If nothing else, Molly Ivins was making this point back in the 1990s, in her inimitable style:
These guys are economic nincompoops; our Federal Reserve Board, composed of people none of us have ever heard of, knows better. They want to slow the economy down, you see. In the world of the Fed (as we cognoscente call it for short), it's bad when the economy grows fast, and it's worse when everyone can find a job. You see. Because these conditions are believed to cause inflation, which the Fed hates worse than anything. Inflation means that rich people's money is worth less and is especially bad for creditors, those make money by loaning money to those of us who have to borrow money. Got it?
So basically, arguments over inflation targets are an interest group struggle: people who make money by loaning it to others want low inflation, because it benefits them. People who borrow money would like higher inflation, because it makes it easier for them to pay the money back.
NOTE: no one is arguing for Weimar Germany/Zimbabwe hyperinflation. This is an argument about whether we should have 1% inflation or 4% inflation.