Saving in a period of high inflation doesn't work if your interest rate is lower than the inflation level. Irrespective of that, inflation definitely has an effect at the extreme ends. If the price of bread increases every hour, you'd better get in line at the shop first thing in the morning. If inflation is zero or negative, then you might consider skipping meals so you can save today's bread money, which will be worth more in the future.

How is this not an inflationary spiral then?

Since the Fed keeps the rate much below inflation then all cash should be spent... which further encourages higher prices!

I just don't see the endgame here except hyperinflation to destroy the currency and start anew.

Indeed, does it work?

Normal folk just save more, reduce spending.