The "are you a permanent resident" question comes into play when the company thinks it will need to spend money on helping you becoming one, or in changing jobs. Many don't want to do that, so if you aren't one, you're out of the running.
hmmm...so how do we fix that? Redefine residency (interim residency) as something that can be more easily attained prior to the Green Card status? Decouple it from the employer?
I'm trying to get to the heart of some of these problems as I hear too much high level rhetoric around things like "just increase the number of H1-Bs". I'm suspicious that these arguments hold well for employers but not so well for the immigrant.
I think the easiest way to fix the problem is to do exactly what you suggest -- decouple a person's immigration status from their employer. I'd do this by scrapping the H1B program and instead simply offer a green card to every person that has a letter of employment from a US company. The government could continue to apply various filters (total quotas, country-specific quotas, educational or experience requirements, language competency, etc). [1] However, at soon as a person is admitted to the US, their immigration status should have absolutely nothing to do with their employer.
Under this system, a company can't pay an immigrant less than their worth, since the person is free to work at any business that is willing to pay more. It also fixes a whole bunch of other subtle problems that come up with an employment-based immigration system.
For example, right now once a H1B holder applies for a GC, they can neither changes companies nor change their job title (e.x. be promoted) without abandoning their GC application. Since this process can take years and thousands of dollars, immigrants are not only shackled to their sponsoring company, but to a particular job (and often pay-level) within that business.
I should point out here that I'm Canadian that may one day be working in the US... so perhaps I have a bit of a pro-immigrant bias here.
[1] Personally, I'd get rid of most of these too, but that is the subject of a different rant.
