Since 1995 the Social Security COLA has increased each dollar of benefit from $1.00 to $1.60.
Since 1995 the CPI has increased at the same rate.
In addition if you look at the PCE (1) which is used by the Federal Reserve, you find that the COLA increases have exceeded that measure. Plus the PCE gives greater weight to health care costs.
So the general assumption that the SS COLA is way off base is not accurate.
Even using the CPI-E for elderly people only changes the calculation by 0.2% over time according to the Social Security Chief Actuary, and based on past history can be lower than the CPI-W (which is used today for the COLA) in a given year.
(1) The personal consumption expenditure (PCE) measure is the component statistic for consumption in gross domestic product (GDP) collected by the United States Bureau of Economic Analysis (BEA). It consists of the actual and imputed expenditures of households and includes data pertaining to durable and non-durable goods and services. It is essentially a measure of goods and services targeted towards individuals and consumed by individuals. Source: Wikipedia