The most successful scams actually do go into excruciating detail to appear methodical, that's how you get people to buy in.

While I do agree with many of the points you raised, for me those point to the uselessness of the CPI as a matric. If the dataset is so complex you can only boil it down so far before too much context is lost. The CPI is an attempt to create a single number of off the entire economy, a task that is impossible made only more clear by complaints over the obvious and egregious tradeoffs made.

Statistics can be useful, it can also be a pointless game of manipulating so much data that you can make it say whatever you want. I think you'd be hard pressed to find an average American that would feel like prices have only gone up by ~4-5% over the last few years.