If there isn't a market for it then there isn't a shortage of labor -- the correct equilibrium point has been found. And yet, they're claiming a shortage. They want to eat their cake and have it too.
I think companies have enjoyed historically high profits for a long time now and are simply loath to give that up. What is a reasonable, sustainable level of profit that benefits everyone? It's certainly not what we've seen for the last decade at least. Profits are sky high and wages are deeply stagnant. I've run my own company for decades and I can tell you there isn't a business person alive who will willingly say in public "we're making excellent profits" no matter the situation it's always doom and gloom and the taxes are too high and the wages are too high and there aren't enough qualified candidates etc.
Profits are not what make wages go down. Profits make wages go up, because then more gets invested and capital competes for labor. We are also in a decade since the recession of record profits, but that might not be so in the next decade or so (from a macro perspective).
Putting a ceiling on profits will not raise wages.