This has been a long standing argument from a certain "trickle down" group in politics. And like the groups that promote austerity as a cure for economic woes, they have been proven wrong.
The economy grows when people can afford to spend. (If this spending is based on credit as was largely the case during the Bill Clinton years, then there is a later cost to pay - no doubt.) But the fact remains that when people can afford to buy things, the economy grows.
Better paid workers spend more money. People who cannot afford basic necessities actually do not blow their money on luxuries as is commonly promoted. Instead, they spend their money on housing, car gas and insurance (since there's been a perpetual movement against public transportation), and food. They're not out gambling and buying drugs in general.
What is not in doubt is that better paid workers means not quite as well paid executives. If you look at the US history, executive pay is at or near the highest multiple relative to workers compared to any time.
And while this is my speculation as I have not experienced living on 1 million dollars vs 100 million dollars (per year), I am inclined to believe that the difference in quality of life is not really terrible. Therefore, executive pay levels are not really a valid reason to suppress worker pay.
We have not even ventured into the tax avoidance that has occurred in the last 40 years. Somehow corporations and executives (and workers!) managed to survive quite ok in the 1950s and 60s, even while corporate taxes were effectively much higher.