The problem with comparing wages by cohort and average inflation is that inflation doesn't affect each cohort evenly. By and large, necessities continue to outpace top line inflation, and they have done so for decades. These include food, healthcare, housing, daycare, and education. Lower income people spend more of their income as a proportion on necessities, so they are impacted more than average by inflation. In order to tell if these lower income people have indeed received wage increases in line with inflation, we would need a model which uses a lower income basket of goods and services.

If I had to put on my tinfoil hat, I presume we don't do this because it would illustrate how badly the poorest are affected by inflation, and validate the frustrations they feel and which are clearly reflected in economic sentiment surveys.

One thing is that 10th percentile wages did barely keep up with inflation from 1979-2019 (0.1% growth annualized), it's only since then that it showed an increase (3.1% annualized).

So it seems to me that any effects along those lines strong enough to exactly negate the apparent real wage growth in recent years must have either 1) been basically constant, so effective wages in this group actually declined 3.1% every year on average for forty years, making 2019 10th-percentile workers reduced to 28.4% of their forbears' wages, or 2) the inflation numbers were about representative for the 10th percentile worker from 1979-2019 and then suddenly and abruptly weren't, or 3) some combination of the two.

(or of course 4), the effect is real, nonzero, but not big enough to wipe out 3.1% apparent wage growth)