Have you listened to Eric Weinstein talk about this? He echoes similar points - essentially cpi is a BS quantity (scalar) when inflation should be represented more like a vector field. It’s like saying the average temperature in the United States is 52 degrees. What does I even do with that information if I live in Montana? A weather map with information dependent on location is a much better description. 

He discusses it in his most recent conversation with Chris Williamson. If that interests you then I will look for the time stamp.