Unfortunately it is really challenging to know what the field as a whole says without undertaking some serious lit. review, but from my understanding their main

Unfortunately it is really challenging to know what the field as a whole says without undertaking some serious lit. review, but from my understanding their main issue with CPI isn’t that you shouldn’t attempt to understand inflation from a quantitative perspective, rather, CPI itself is but one (imperfect) measure of inflation. The “true” value of inflation isn’t perfectly observable, and further, from a policy making perspective, because of its limitations, CPI shouldn’t be a be all end all target. One should look at other measures, such as economic growth and unemployment (inflation after all, occurs when the money supply grows faster than productive capacity). Perhaps that’s “qualitative” by some definition, but it seems to be that it’s more just a case of goodhart’s law. That’s the best I can gather at the moment.