Non-increasing wages is a statistical mirage, not a statement which is a truthful depiction of on-the-ground reality. The overwhelming experience of actual, countable persons is that their wages have increased substantially. The only reason this does not raise the aggregate wage is because too many people have increased from $0 to a number which is, relative to the average, low. (You occasionally see this in larger economy statistics, often as a result of immigration, by the way. "Wages are frozen since the 70s!" is not all that true -- wages are way up for Mexicans who are now Americans, mildly up for Americans who are still Americs, etc.)
Although your argument could be correct, I am unconvinced:
Everyone sees their wages increase substantially, as they gain experience. This does not mean that wages are increasing.
Inflationary effects should be taken into account - wages should at least increase with inflation. Everyone seems satisfied to receive a 5% pay increase, even if that is a freeze in real terms.
If wages were indeed frozen since the 70s, your actual countable people may not notice due to the above two effects. I gather that you understood that, but I thought it worth making clear.
Your argument boils down to the idea that wage figures are biased by the fact there are more new entrants into STEM careers than there were in the past. Do you have evidence for that? I suggest (based on the graduate figures) this may not be the case.
On your point about Mexicans creating low paid work:
I would assume that immigrants are now doing jobs that Americans used to do - so it's not that they have created additional low paid work that biases the statistics, it's just that they have taken over a portion of the low paid work.
So, I think this should not be taken into account in the stats.
It's unclear whether immigrants are doing jobs that Americans used to do, or whether additional low paid work was created. I lean towards the latter, but I don't know how to prove it.
However, the data does show that when you restrict the data to Americans with American parents, incomes have risen for everyone outside the top quintile.
