Why involve companies at all? The visa should be tied to the individual, not the company. The goal should be to enable immigration of skilled/motivated people to the US.
The only role that appears to make sense for corporate involvement is that perhaps a company could select from individuals who have applied and are awaiting entry.
That would be a completely different visa program, and there are alternatives already. The purported goal of the H1B program is to enable companies to bring in foreign labor when they can establish that there is a labor shortage in certain specialized occupations. That was the legislation that was passed by congress. Of course we've found the actual administration of this program does little to meet those goals.
The only role that appears to make sense for corporate involvement is that perhaps a company could select from individuals who have applied and are awaiting entry.