Somewhat disagree. You mentioned the reason, so you're clearly familiar with the counter-argument. The idea is getting paid what you're worth. It's easy to look at certain salaries and say they're getting paid too much. But a deeper dive reveals that sometimes executives really are worth millions to their company.
At my company - which is very much in corporate America - continuity of leadership is sacred, because the company's equilibrium is paramount to keeping tens of millions of dollars in business each year. If there's shakeup in the C-Suite, it's the top headline throughout the industry. And even when it's planned - say there's a prominent CEO retiring - there will be a press release rollout announcing it months in advance, and they usually step down to an advisory role that's still on the payroll, to make sure nobody gets spooked. So a CEO who doesn't technically do 50x more than the entry level employee is still worth 50x more to the company (or likely far more than that). And if you don't pay those people, they leave unceremoniously to companies that WILL pay them, which creates unintended change that can send the company into a spiral.
It's interesting you mention sports coaches. It's the same thing there. A thriving football program with great recruits, consistently prominent bowl games, winning record, etc. etc. is worth a TON more in alumni and merchandising revenue than what the coach is paid. There's an argument that Nick Saban is underpaid.
We don't want to think the common worker - the "backbone" as you put it - is replaceable. But the vast majority are. So it's psychologically infuriating (and I've been in some sh*t jobs for too long, where I'm a replaceable cog among many, so I don't just say this in the abstract), but that doesn't change the reality. However, outside of downturns like 2008, this happens on a smaller scale for every position. "Pay them so they don't leave" can and does apply to even the entry levels workers, provided they prove their value to a company. Some will have more, sure, but it's not a zero-sum game.
Higher tax rates on the rich and, say, subsidizing to living wage and providing more funding for educational programs to bring up the bottom tiers of the socioeconomic ladder are great. I'm all for them. But I'm not sure less pay for execs is feasible in a capitalist system, or that it's in fact the central problem surrounding wealth disparity. Someone will always be willing to pay more to entice high-profile hires and will reap the benefits.