Fundamentally, though, the problem is that CPI does not track changes in the perceived minimal acceptable quality of the various baskets of goods. If the house you "need" to fulfill a specific lifestyle is twice as big and twice as expensive, this has zero impact on CPI. Same with healthcare quality - if your insulin works 10% better and costs 10% more, the CPI-centric view says that people are simply using more real dollars to buy a higher quality of life. Education has a similar problem, where job requirements shifts from high-school diplomas to undergrad degrees simply do not show up in any way in the CPI; we're just choosing to be better educated to end up working the same jobs.
I think this all boils down to the CPI measuring things as if all goods were absolute goods, while nominal GDP per capita would be the appropriate measure if all goods were positional. I don't know what fraction of spending is on each, though, but you can reasonably put the "real" inflation number somewhere between the two.