This assumption comes from evidence in our not-so-distant past. In the 1940s-60s, income was taxed at a much higher rate in the higher brackets (50-80%+ depending on the time); this served a similar function of the executive pay cap in your hypothetical. After the highest earners in a company reached the top brackets, it didn't make much sense for the company to further increase their pay (much of it would be lost to taxes so the ROI wasn't great).
So now you have all this leftover profit that, in 2018, would have went to CEO pay or bonuses. What is there to do with it? Invest in the company of course: give the best performing line-level employees raises, start internal training programs, kickstart moonshot R&D ideas, and so on.
(Unions also helped in ensuring that the rank and file got pay increases commensurate with management's raises)
Don't get me wrong, the highest earners were still very wealthy (and had plenty of yachts/summer homes/other symbols we associate with the 0.1%) and it was common to give them raises every year, but the higher marginal rates really did help in "forcing" profits downward.
"We took all the increased profits, so there's none left for you."
We're seeing increasing profits, increasing wages for high level management, and static wages for most employees.
The second isn't an intrinsic issue itself, but we don't have just the second, we have all three, and _that_ is the problem. If profits and wages were both stagnant, then we would be having a different problem, but that isn't the world we live in. We live in the world where profits are going up, and all of it is going to people other than the workers.
Yeah, it does. Money given to bosses and shareholders is money not available to pay workers.
To be clear, my issue is not that workers shouldn't be paid more, it is that justification for higher worker pay shouldn't be "my boss gets paid more than me."
Since you're being downvoted without any responses, I'll try to add my take. To me, it's not that a manager is getting paid more. It's that he's getting paid 312x more when the average worker in America struggling to afford healthcare, an education for their kids, and probably has to take in two salaries just to make ends meet. That's when income inequality is a problem -- when it's so unequal that one side gets everything, and the other is left to a battle royale.