Have you looked into how CPI is calculated? It's not that it's "incorrect", just that it doesn't reflect the challenges that real people face trying to afford the basic expenses of life.
I find his COTI quite misleading/confusing. It seems he is counting 100% of health care expenses (100% of premiums) but not counting the ~70-80% of premiums an employer pays the median employee in median weekly earnings.
In the college field, he also uses a semester if college tuition for some reason. Since this is a 1 time cost, it should almost surely be accounted for differently.
In his article he defends all of the choices he made for the COTI calculation. 100% of the premium is used because most people in 1980 paid for the whole thing themselves. I guess it raises the question that the institution of employer sponsorship allowed the costs to balloon, but that is a whole different discussion.
