This long period of quiet inflation at the zero bound - and Japan's longer period - poses a deep challenge to monetary economics. Old-Keynesian models (including Milton Friedman's 1968 AEA address) predict inflation is unstable under a peg. They predict a deflation spiral, which did not happen.
I don't believe this is accurate. Friedman believed that an interest rate peg would be destabilizing when changes in the money supply were being used to keep interest rates fixed. That does not describe recent policies in developed countries.
Friedman was concerned about the following scenario. Suppose the economy strengthened (higher NGDP growth.) That puts upward pressure on interest rates. The Fed injects more money to hold interest rates at the peg. But the extra money causes even faster NGDP growth, which puts even more upward pressure on interest rates. The Fed injects even more money, etc. etc. In a few years you've become Zimbabwe.
Of course central banks never do this, as it would be foolish. Even the Zimbabwe hyperinflation was done for unrelated (fiscal) reasons.
The zero bound is quite different from an interest rate peg. Instead of using changes in the money supply to keep interest rates fixed, they rely on the inability of rates to fall (very far) below zero. Rather than using interest rate targeting, central banks target the inflation rate by adjusting the money supply. The BOJ moved the money supply up and down to keep inflation close to its target of 0% from the mid-1990s to 2012. Inflation rose to about 2% over the next few years, after Japan raised its inflation target to 2%. (But inflation has recently fallen back to zero, as the BOJ seems to have given up about a year ago.)
Macroeconomists keep insisting that recent events are inconsistent with modern macro models. If so, then maybe they are looking at the wrong models. I don't see any mysteries that need explaining. Recent events are easily explained within the market monetarist framework.