"My plan would hold prices for 10 years, thus eliminating inflation."
That is not a realistic concept, as in not part of reality. It's not simply impractical. It is no more real then expecting to eliminate gravity. Inflation is a necessary and required part of the way the economy functions. It has to be held low, but not zero. The other option in deflation. To put it simply, deflation is very bad. During the Great Recession, the rate of inflation fell to -3%. This was because people stopped buying things. Prices collapsed as did employment and the economy.
It is impossible to hold the percentage change in the CPI, or any measure of inflation, to zero. On a quarter to quarter basis, the rate of inflation varies from as much as -0.8% to as much as 1.7%. The average yearly inflation for the last eight years was 1.9%. In 2015, the rate was 0.4%. For 2017 it was 2.2%. These rates are actually quite remarkable considering that in the decades of the 1970 and 1980, the yearly inflation rate hit 12.64% and averaged about 6% per year for the entire 20 year period.
The Federal Reserve has just three goals, maximize sustainable employment, stabilize prices, and moderate long term interest rates. These three are intimately connected. They have managed to hold inflation to 2.1%, 1.8%, 0.41% and 1.2% for the last four years. There is no plan that is going to do better. That is as close to zero as it's gonna get. Attempting to make it zero would be a disaster. Employment would suffer. It wouldn't be maximized. It would fall to less than maximum. And there would be an all to real risk of it collapsing as it did during the Great Recession.
The problem isn't inflation. The problem is elsewhere. The problem is in the lack of consumer savings. And while it may seem like no inflation would result in the ability for the average person to save, it wouldn't.