This is a huge disagreement between us. If you loosen immigration in general, then you may have freer markets. But if you loosen them only in a narrow segment of the economy and while restricting mobility in others, you may end up creating severe market distortions that don't resemble a free market in any way.

If almost every country and profession had equally liberal immigration policies, then yes, I'd agree. But we're not doing this evenly, and I think this is why so many people who hold a favorable general view of immigration nonetheless object to these targeted visa/green card programs. As it stands, I think that adding a green card to every STEM degree (but not every JD, MD, MBA, DDS, etc) will end up creating market distortions that will probably just further deter US citizens from entering this field, amplifying the cycle of "shortages" and perhaps eventually creating exactly the "crisis" that the policy is intended to address.

There is an externality to letting in more people though. The hiring companies get all the upside in form of more workers, but the public as a whole takes on the downside risk of supporting them if they're unemployed, retraining them if they're unemployed, integrating them culturally, etc. The public commits to educating those peoples' kids for free for 12-13 years and at subsidized prices for college, supporting them if they ever use welfare services, etc. It's not a clear cut: "more free, less free" situation, but a "who pays for it?" situation.