Another thing to consider is that a 'dollar' was consistent in name only over that period.
until 1900: A dollar represented a weight of gold and silver
1900: $20.67 / oz gold
1933: $35 / oz gold (internationally only, domestically it was just a piece of paper)
1971: (outside of the 70 year range) USD represents only the full faith and credit of the USG
So observing that a coke cost a nickel throughout that period is interesting - but the dollar isn't really a static denominator of value over time that it might appear to be. Certainly using basket of goods is necessary after 1971 because since 1971 a dollar is nothing more than an idea in people's heads. It has no guaranteed exchangability for something (real) from the currency issuer, it's value is only derived from what other people are willing to exchange it for that day.
The fixed price syrup story is interesting though - just goes to show how a different mindset on the inflation risks of the currency were back then.