Same labor shortage as everywhere that the government likes to pretend doesn't exist. 10 million working-age men can't or won't work. Of the ones willing to work, almost none want to spend their time learning skills for back-breaking, barely-middle class skills jobs which they'll be forced to retire from at 55 because their knees give out. Same answer for the shortage as everywhere that the economists don't want to h…
As you say in your post, paying more might do it. I’m sure businesses would pay more if they needed the employees and could profitably employ them at a higher wage. Surely they’d rather make less money per employee than not make any money. So, they must not be able to pay more than they are.
We could lower the minimum wage; maybe there are employers who would employ those 10 million men if they could do it at a lower cost, but still the workers wouldn’t be willing to work any more than they are now.
That leaves raising the opportunity cost of not working, e.g. not paying people who won’t work as much to not work. That’s the answer that the people who have answers “that the economists don’t want to hear” don’t want to hear. UBI/negative income tax or cutting welfare programs would help those folks get jobs, but with the risk that some might not, and would end up on the streets.