Cool that you posted a Pew Research article, they tend to get rarely shown and are often well substantiated. This one, maybe a bit less (5,200 adults vs the usual 10,000 survey respondents, yet still pretty substantiated.
Within the article, the education part definitely differs by gender. For males, the college degree has been oscillating upward, downward, and flat over the last 50 years. 75-85 semi-down, 85 big jump, mostly flat till mid-90's, rose till maybe 2002, yet then down till 2015. Finally up in the last decade.
Also, in comparison, without a degree has been uniformly horrible for the most part, with down or flat for 40 years (except maybe the bump in mid-90's). (Provides a big push to get a degree, probably get a lot of "don't do what we did, go to school")
Women on the other hand, after the drop in 73-74, have had almost nothing other than upward or flat for 50 years from getting an education. $40,400 to $65,000. Without a degree has mostly been flat. The story for them is "get a degree, it enables earning (and probably independence). Creates very different views and kind of a strange gender dynamic in the discussion.
On that, it seems like a possibility that the last decade trend (and a lot of the manosphere stuff that's shown up recently) may have been when the High School or Some College crowd male pay started approaching the High School or Some College female pay. Personal opinion, yet it seems likely to set off lots of societal issues about family breadwinner, provider, head-of-family, ect...
On the original topic of the post, "If employers provided training and did not require a degree", this likely works for many jobs, and I agree there is probably a lot of false "check-the-box" requirement nonsense in the job market. However, there are quite a few jobs where the starting tasks presume that you have a significant amount of prior familiarization with concepts. You actually use semi-complex math (derivatives, integrals), you need to demonstrate significant skill in liberal arts (production concept art), you need to be familiar with a relatively complicated system with lots of fine details (legal, laws), ect...
There's also an issue in there somewhere, that if the jobs are so simple that all they require is walking in the door and getting training, then those jobs are: relatively low actual skill required, likely limited creative personal input needed, and probable for replacement if there's a way to replace it with tech. That said, the trainee/novice, apprentice, journeyman, master thing has worked since probably the middle-ages in a lot of fields, so there's possibilities.
Also, my standard reply to lot of these issues that's underneath much of the American education "Loyal workers are selectively and ironically targeted for exploitation" https://www.sciencedirect.com/science/article/abs/pii/S00221... The issue being that you go through all this education, and then work in an environment where your diligence is mostly exploited, and you simply get extra work for being skilled, while people who just faked it get promoted.