Fair enough. There still seems to be a disconnect though, as the cost of various goods, such as housing, have far exceeded inflation. Are there any charts that try to track wages against a basket of goods?
That's what the CPI is and the real wage growth charts are exactly what you're asking for.
That being said, there's definitely a disconnect. The CPI metric is constantly changing, and is such a broad economic indicator that many people's experiences will not "feel" like what the federal data suggests.
The root of the growing wealth gap is the massive deficit we've been running. Especially since the GFC, the strategy has been to rack up a bunch of debt and inflate that debt away. This inflates the value of financial assets, property, and commodities...none of which is owned by the average joe whose cash savings gets destroyed in the interim.
I agree with everything you say except for one point:
> none of which is owned by the average joe
About 66% of US households "own" a home (often with a fixed-rate mortgage, which makes rising inflation doubly good for those homeowners) and 58% of homes are owner-occupied. The median Joe is a homeowner, not a renter.