Zero inflation is fine, but a small hiccup would cause it to spiral into deflation. Deflation sounds good in a micro-scale because money gets more valuable. However, this is actually a terrible thing because the only way this can happen is when money gets destroyed through defaults, which is why you only see deflation during a financial crisis.
When technology increases increases productivity and society has a fixed supply of paper money, you'd think you'd see deflation because there are more goods and the same amount of money. However, actually during those periods of times, banks lend out money, which increases the money supply. This is a good thing because they're enabling economic activity that otherwise wouldn't have happened like a loan to start a new business. However, this system is fragile because if depositors lose faith in the bank, everyone will try to withdrawal their money, which is called a bank run. The bank doesn't have enough money because they leant some of it out, so they default and depositors that aren't quick money lose their money. One of the purposes of central banks is to ensure that this doesn't happen.