It's not cherry picking when wages have been stagnant for the last 40+ years.
Here is a more complete picture, with words and discussion and multiple graphs too: https://www.pewresearch.org/fact-tank/2018/08/07/for-most-us...
There’s a story to tell here, but you’re not showing it.
Roughly, the way it "should" work is that if Company A and Company B are in the same industry, and Company A is more productive than Company B, free market forces cause Company A to pay more than Company B, thus improving their ability to compete for workers. Generalize this to an entire industry of competing companies, and then to an entire economy.
Refuting the (willful) abuse of statistics is like trying to refute numerology with reason.
Even here there is a definitive and deliberate bump right during the beginning of the COVID times. I don't believe that's an artifact. Somehow this analysis is saying people are vastly better in August than they were in February.
I think that "average" in most of the different versions is useless. The millionaire and billionaire classes can be so over-represented they can draw the rest up. It doesn't answer if all of society is actually becoming more well off or just the cream continuing to rise.
If I could go to my landlord and trade them a months' worth of health insurance benefits for rent, then you'd be on to something. If you could find a way to separate out the part of "total compensation" that actually contributes to income, such as stock grants & such, then we could talk. But, just "total compensation" doesn't cut it.
If you really want to get a true picture of how screwed the American worker is, take a look at housing and education costs over time, as well. Both have increased faster than inflation, and vastly outpaced wage growth; yet everyone needs a home, and a college degree is practically a requirement for any vaguely middle-class career.
If you want to look at the "value" of, say, an employer's group health insurance plan to me, what you really need to look at is the difference between buying the exact same coverage as an individual versus participating in the group plan. This is not an analysis that can typically be performed, because insurance companies don't want you to be able to compare on price like that. But, assuming you could, if I got, say, a $100 discount per month, and I was going to buy that coverage anyway, then, sure, you'd have a good case for calling that +$100 on my balance sheet.
Over time, which is what we are talking about here, the choice of the employer to put money into benefits in order to create an attractive compensation package means they are not putting money into wages (assuming for simplicity that those are the only two buckets to consider). So wages can stagnate while total compensation goes up.
Yes you can conclude from this that your take home pay is stagnant, what you can't conclude is that there hasn't been an increase in compensation. And if you are trying to determine if compensation is correlated with productivity gains (i.e. the original article) then you can't just pretend those benefits aren't part of the compensation equation.
Again, I literally don't care what my employer spends its money on in this calculation, other than my paycheck, and discounts on things I would use anyway such as health insurance they pass along from bulk buying. So, you can't say, "well, if they didn't offer insurance, and instead passed along savings in your paycheck, then your income would increase." Yes, I still need to buy insurance, so only the discount I get from obtaining it via my employer is relevant -- my literal bottom line does not change. (Actually, my bottom line is worse in this scenario because I don't get the tax break, but let's just ignore that). And, if a benefit isn't something I would use (let's say a childcare allowance, if I don't have children), that also goes on the company balance sheet and could potentially increase my "total compensation," but literally does nothing for me, hence its value to me is $0.
You seem to be talking past my point, which is that the American worker is getting screwed from all sides by stagnating wages and skyrocketing healthcare, housing, and education costs. In America, for most employees, those expenses come out of wages, so wages are what we ought to be concerned with.