Going through the Wikipedia article on inflation, a number of pros and cons to inflation are covered. Most of the "cons" of inflation (cost-push inflation, hoarding, hyperinflation, diminished allocative efficiency, etc.), don't become a problem until inflation is well above the levels currently targeted by The Fed.
A number of "pros" are also covered, but one I don't see addressed anywhere I've looked is this: the average U.S. household debt is 3x the average annual income. Our government is also in debt to the tune of \$21T, which comes at a cost of \$400B per year in interest paid. I do see acknowledgement that higher inflation eases debt, but nothing on why increased debt hasn't incentivized us to increase inflation.
Wouldn't a higher inflation rate be a good thing? It would devalue those (household and federal) debts, making them easier to pay off, and saving the interest paid for other budget items. If the Government (and most Americans) were running closer to the black, I can see why you'd want to keep interest low, but given the unprecedented situation, why not allow inflation to float higher?