Surely putting together an inflation index consciously designed not to replicate an average American diet would be a much, much worse measure of food inflation than one that does actually try to model the average American's situation? "Everyone should be going paleo so the index shouldn't have bread in it" is a self-evidently bad idea, that's not a statistician's job. A single inflation number is hardly ever going to be a correct measurement of any single person's experience of inflation, but that's inevitable.

There are real criticisms to make, such as the average basket of goods not characterizing the inflation felt by the poorest, because they spend money on different things than people with a bit more money.