You’re correct!
But you forgot one thing: If they become legal, and employers have to start paying for all the things legal employees require, ( like workers comp insurance, 15% FICA, etc. ) they have lost their attractiveness to the employer.
The employer will then go looking for someone else to work “off the books”.
I think the whole premise that this will get them to “come out of the shadows” is false.
Actually, most of them are paying FICA, and they’re covered by Worker’s Comp.
They are on the W-2 payroll at most companies. They’re just using someone else’s Social.