They seem to fail to capture a whole lot of things. Supposedly $1 in 2000 is worth $1.88 in 2025. So 88% inflation over the 25 years. Meanwhile the median home price has increased by 150%. Family insurance by 350%. Median college tuition by 225%. Childcare costs have risen by 200%. But sure. We can buy super cheap 65" tvs now. Hurray for us! Literal kings who lived hundreds of years ago couldn't possibly imagine a world with cheap large screen tvs. So the poorest among us should rejoice at the wonders they are able to enjoy while they skip meals and ration their insulin.
This explores the ideas behind your post: important things, like education and healthcare, have disproportionately risen in price while not-so-imortant thing have gotten less expensive.
https://www.yesigiveafig.com/p/part-1-my-life-is-a-lie
I don't exactly agree with the numbers, but I think the basic ideas are true
A dozen eggs is up over 350%, but a 6-pack of Budweiser is only up 60ish% since 2000. So you know, it all balances out. Maybe drink a few extra cans of Bud with your next meal.
The inflation basket only represent a hypothetical average person, who doesn't even exist.
It's more useful to construct multiple separate inflation measures that represent different types of people. Like a "typical renter" inflation figure vs a "typical homeowner" inflation figure. It wouldn't be hard to do and would shine a light on inequality and help explain the rise of populism in certain segments of society.
An even better measure would somehow appropriately normalize the figure by the average disposable income in each of the segments to come up with a figure that measures the felt impact better.
The figure would be negative for wealthy people (who actually benefit from inflation because of asset price inflation) and positive for poor people (whose disposable income mostly goes to rent).