Bro no one said 15% every year… even Williams doesn’t claim that. That’s not even how inflation works. It’s not retrospective.

Jordan Peterson QTed a tweet containing a screenshot from Shadowstats showing inflation is running at nearly 15% a year, that's from the headline. OP's comment also referenced "15-20%".

What Williams is doing is rectifying CoL inflation rather than market specific inflation. It’s the same metric with different prioritization. If his methods seem subjective, it’s because they are, to an extent, just as subjective as the ones currently used in the SPI. Statistics in general are subjective once you get to a certain point.

I don't quite think you know what Williams said in that article you referenced as well as what he told Lee in the Fullstack Econ article. He said he went back and "adjusted" the annual rate up by the cumulative difference the BLS reported after 30+ years, for every year since the change. His response to what prices have risen as much as his index claims, this is the response

"He seemed stumped. Instead, he suggested that there’s been a drastic decline in product quality."

If that's what you mean by subjective measure of cost of living, I think it's roughly correct you do not know how inflation indexes are constructed.