The important part is the segmentation of inflation between the whole economy (consumer goods, industry, and also the basics) and the price of just the basics: housing, health care, transportation, education. If those basics were the basket of goods used to define inflation, then the numbers would be very different.

$1000 in 1985 dollars buys $2300 worth of consumer goods in 2020. But you'd need $3,110 2020 dollars to buy the basics you could get for $1000 in 1985.

Also, another aspect to consider is what is the basic minimum to be integrated in society and exist socially.

In the 20ies cars were not a social necessity, but beyond the 70ies, not having a car generally means partial social exclusion (more difficulties to get a job, etc).

Today, not having a computer/smartphone/tablet and an internet subscription would impact social integration.

This basic minimum need is not set in stone, it's a shifting target. Rephrasing the problem with "What is the current median revenue Vs What is the basic minimum to be an integrated member of society" would be a better way to put it.

Or, in other words, inflation indexes are an average, and like all averages, it's a bad idea to blindly trust it, because sub-groups of the overall data may show much different results.

The problem is not averaging. The problem is these inflation measures specifically exclude major expenses.