Applying a cost-of-living escalation COLA clause to a stream of periodic payments protects the real value of those payments and effectively transfers the risk of inflation from the payee to the payor, who must pay more each year to reflect the increases in prices. Thus, inflation indexation is often applied to pension payments, rents and other situations which are not subject to regular re-pricing in the market.
COLA is not CPI which is an aggregate indicator. Using CPI as a COLA salary adjustment for taxable income fails to recognize that increases are generally taxed at the highest marginal tax rate whereas an individual's rising costs are paid with after-tax dollars - dollars commensurate with an individual's average after-tax level. Indexing tax brackets does not address this fundamental issue but it does effectively eliminate "bracket-creep". Indexation has been very important in high-inflation environments, and was known as monetary correction "correção monetária" in Brazil from 1964 to 1994. Some countries have cut back significantly in the use of indexation and cost-of-living escalation clauses, first by applying only partial protection for price increases and eventually eliminating such protection altogether when inflation is brought down to single digits.
Protecting one of the parties from the risk of inflation means that the price risk must be shifted to another party. For example, if state pensions are adjusted for inflation, the price risk is passed from the pensioners to the taxpayers. But the taxpayers may be protected as well, if the income tax brackets are routinely adjusted upwards in order to keep from having to pay more taxes just because of inflation. So, if the pensioners and the taxpayers are both protected from inflation, who is bearing the price risk ultimately? The higher pension costs have to be financed, probably by long term public debt. If so, the inflation risk is probably being passed to the "grandchildren of the taxpayers" who will have to repay it.