There is one obvious flaw with this argument: it misses much of the point. If we were really terrible at measuring inflation in this way, then yes maybe most peoples' income has actually increased. But the bigger issue is that the top sliver of the income distribution has made steady gains since the 1970s even using this potentially underestimated measure of inflation. If we are underestimating the gains for most people we are also underestimating the top part of the distribution's large gains as well. Reinforcing the point.
Ok, but what about this idea that we underestimate inflation because we have a difficult time correcting for improvements in the goods that people buy. Maybe there is something to this, which I'll follow up on later. . .