Your not taking about an inflation index thec, but a cost of living index. And they are not the same thing. There are many reasons the cost of living can change

Your not taking about an inflation index thec, but a cost of living index. And they are not the same thing. There are many reasons the cost of living can change without a change in the currency, such as a change in the preference of goods or technological advancement in a particular field or price controls or regulation. If you are going say "but the CPI does measure things that way" you are right. It has been well observed that the CPI had been looking more and more like a cost of living index for years (eg, the hedonics changes). This is why the GDP deflator is used more often to gauge inflation now, except it only come out quarterly with the GDP figures.