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I think you're making the same mistake.

It does not depend at all on people's mandatory expenses remaining the same items, just that the inflation metric captures the increase in their expense overall.

Do you agree that the 3x food was roughly accurate in 1963? If you do, then it doesn't matter at all how the number was calculated. Because we're not re-doing the same calculation with modern numbers. We're instead just increasing that number by the inflation rate.

I agree that some of those things have increased much faster than inflation, but some things have increased much slower than inflation, and necessarily so, or the inflation metric itself would be much higher. Like food. Food has gotten a lot cheaper, which cancels out some of the increase in housing prices. Inflation overall gives a much better assessment of the increase in the cost of living than the author gives it credit for. It's certainly not perfect. It might be missing some overall rising costs by including the decline in prices for non-necessities. But that effect is much smaller than 5x that the author claims the metric is off by.

Edit: I'm not arguing that the poverty line calculation is good, or an accurate assessment of the minimum cost of living. I was just annoyed that the logic that the article was using to argue against it was flawed. (In addition to their use of incorrect quotes, averages instead of medians, etc. Averages in particular always is frustrating since income inequality is always also a big point people make, and that necessarily means that average cost of say rent or a home will be skewed high)

To be fair, I did only read about the first 1/3 of the article before I got too annoyed at it and checked the HN comments to see if anyone had the same frustrations I did. I've now gone back and read the whole article, and my skepticism for their numbers/calculations remains throughout. I agree with their point generally, that there's a benefits cliff that undermines the effectiveness of the social safety net, but the way that they get there feels like them pulling numbers out of nowhere.

Also, you're still making the same mistake that the author did by saying that it assumes that other variables remain static for 60 years. That's not how this calculation is done. The previous value is multiplied by the change in CPI, which is a measure of the inflation. That inflation measure includes increases in housing, food, etc. Which is the way in which those other variables are coupled back into the metric.

Your horse example actually demonstrates this, but in the opposite way to what you're saying.

Imagine that 3x horse expenses was a really good metric for how much you needed to survive in 1910. Let's say that worked out to 1k a year (making numbers up). At this point we don't have to care how this number was derived, since it's a really good metric for the poverty line in 1910. Now we take this 1k number and multiple it by the inflation since 1910. Not the inflation in horse maintenance costs (which would be what you're describing), but the general inflation overall. We arrive at some number. Horse maintenance is now essentially 0% of the average cost of living, but that won't make this metric incorrect. Imagine that the metric was instead based on 10x the cost of clothes. And that also worked out to about 1k. It's not like when we multiply this 1k by the CPI change, we're going to end up with a different number than the 1k*CPI we got from horse maintenance costs. How the original number was derived is not relevant to its current accuracy. This is the fallacy that both you and the article are making.

The more correct question to be asking is why does CPI not account for the cost of living changes we see. Not dunking on a formula because you misunderstand it.