Perhaps I am economically naive, but why does there need to be any inflation? Why isn't 0 a target?
When banks make a bad loan and are forced to write of the loan each dollar of loss results in 11 less dollars of loans that can be made. When this happens to a lot of banks at the same time you get a general decrease in the money supply and general deflation (like the Great Depression).
A positive rate of inflation allows banks to resolve some bad loans simply by holding the loan until inflation increases the asset value above the loan amount rather than a write-off. Positive inflation, in other words, is a lubricant for the banking system to make it easier to resolve bad loans which makes issuing loans simpler.
With zero percent inflation banks would demand higher standards for underwriting such as stronger credit and larger down payments. that would generally mean loans would be directed mostly towards older, larger and more established industries and less to newer and smaller industries. Less loans for young people and more for older people.
As a side note what makes the Federal Reserve special is that it is allowed to make loans with infinite leverage on capital. That means instead of a 1 to 12 ration of a typical bank it could be 1 to 100 or 1 to 1000. To keep this special position any profits are foreited to the U.S. Government and implicitly any losses are also eaten by the U.S. Government as well. Which is why which assets the Feseral Reserve purchases is a sensitive topic.