Businesses would squawk because this is their own money you think is being devalued, and they need to be able to make decisions about future plans based on real inflation, not cooked inflation. Believe it or not, sometimes the consumer participant and the business participant have interests which do align. Think for yourself: If you were in business, wouldn't YOU want to know what the real inflation rate was?
These numbers are developed primarily for business consumption for decision making. There is no business interest (except in isolated cases) that is served by cooked economics statistics, because it would lead to bad decision making.