Thanks, I do get that. However, what I am arguing is although the core CPI is a better measure of the Feds influence, that influence might be over an economy that represents a shrinking number of Americans. You can keep the 'economy healthy', but the 'economy' that you are keeping healthy might be shifting towards a subset of the population. For example, GDP can be great, but be due in large part to 40% of the population, or be great and be in large part due to 90% of the population. The core CPI might be something that can be better pushed and pulled by the Fed, however, the real question is how much that matters to the majority of Americans, for which the Fed works for. It could be argued that as disparity grows, the core CPI might be more easily manipulated, and yet less meaningful to the broader population. What confuses the CPI even more, is that those components that are included in the CPI are weighted by the Bureau of Labor Statistics, and they don't necessarily reflect the changing importance of the components. As a college education has become more necessary to get a good wage, and as healthcare costs have become more likely to be able to cause bankruptcy, it's tough to say that inflation has remained low for a family buying heathcare out of pocket and sending kids to college over the last decade.
Your right about the components. The average doesn't really mean a lot. The basket of goods consumed is different for age groups, income groups. There can be effective inflation for one person and deflation for another. Each of us needs our own CPI, really, when you get right down to it.