Yes, that scenario is bad and it happens when the Fed is still trying to control inflation.
The people who presented as arguing for 0% inflation are actually more often arguing for a lack of inflation targeting at all, and an end to the practice of creating money. In other words they argue for 100% reserve banking and abolition of the legal right of the central bank to issue new money.
In such a system prices might go up or down, depending on whether the underlying economy is doing better or worse, and governments would simply ignore it. In the case of demographic decline that would mean prices do indeed go up and that would correctly reflect the fact that resources have become scarcer.
The people who presented as arguing for 0% inflation are actually more often arguing for a lack of inflation targeting at all, and an end to the practice of creating money. In other words they argue for 100% reserve banking and abolition of the legal right of the central bank to issue new money.
In such a system prices might go up or down, depending on whether the underlying economy is doing better or worse, and governments would simply ignore it. In the case of demographic decline that would mean prices do indeed go up and that would correctly reflect the fact that resources have become scarcer.