Low inflation has huge potential downsides in that fiat money can't have negative nominal return while it is quite normal for private investment returns to go negative sometimes (thermodynamics says that things, including stores of value, tend to degrade with time unless you put work and energy into them).
This is the famous zero lower bound problem. It means that when private market rates go negative, people transfer their savings to cash, the world switches from producing real stuff and building real businesses to people hoarding intrinsically worthless pieces of paper (pieces of paper that might not be able to buy that much in the future because production will have gone down.
On top of this, if you keep interest rates above market rates and inflation too low for a long enough time, that is if you keep rates high at 0% when they should be at -3%, market pressure will build for an uncontrolled inflation rebound when all the cash hoarded on the sidelines start flowing in an economy with lowered production. It is much easier to keep inflation stable if you keep it high enough so that the investment market can always clear and never hits the zero lower bound.