This is a very real and genuinely alarming phenomenon that it's important not to overthink. Look at that huge increase in the labor share from 1996 to 2000 and you'll see what you really need to know. That's not a time when Americans grabbed their pitchforks and burned down the mansions of the rich. Indeed, as I recall it the rich were actually doing quite well at the time and the stock market was soaring. But the average wage earner was also enjoying a great run because unemployment was super-low.
It was a crazy time. The way it worked was that if you weren't happy with your job, you could just quit and find a new one. Which meant that if your boss was earning fat profit margins, you could credibly threaten to quit and get a raise. That was great for people who got raises, but it also had awesome knock-on effects all across American society. Some people, for example, were in industries that were genuinely low margin and couldn't afford to hand out raises. So experienced workers would quit those jobs, and low wage employers had to invest time and energy in pulling whole new people into the labor market. It was raises for the previously employed, and new labor market opportunities for folks (high school dropouts, ex cons) who'd be considered "unemployable" today.
And it got even better!
In the face of persistent labor shortages and needy demanding workers suddenly it was clear that productivity improvements rather than hard-ass bargaining was the only viable path to higher profitability. And so productivity rose! Rather than endless rounds of givebacks and lockouts, managers were accepting the need to pay people or lose staff and focusing on finding ways to get more output. It was awesome.
For a more technical treatment, I'd refer you to Jared Bernstein and Dean Baker's unjustly neglected 2003 book The Benefits of Full Employment: When Markets Work For People but suffice it to say that full employment—specifically policy that doesn't just pay lip service to the idea, but is actually wlilling to run some risks of possible inflation in its pursuit—is really great. It's especially great for working people, as seen in that chart, but part of what's so amazing about it is that it's actually pretty great for everyone.