Unless you can point to a reason why law of supply and demand was breached, high salaries reflect high demand vs. low supply and low salaries reflect low demand vs. high supply.
My understanding is that healthcare and pharma are not exactly poor industries so if they don't pay their highly skilled workers a lot of money, the most likely explanation is that there's abundance of those workers.
What follows from that is that we don't need to import them from abroad.
And that logic generalizes to all industries hence it really is that simple as letting in those who can score the highest salaries.
It aligns the interests of U.S. in general (highly paid workers put way more into taxes than they get back in benefits) with the interests of the companies.
It's hard to game, simple to apply and trivial to verify (once you issue SSN you check with IRS once a year if they are really paid what the company said it will pay). And if companies try some fraud they are now in the business of tax fraud.
It boggles the mind that this is not a rule applied by all governments in the world. Unless, of course, you understand that government is not exactly pre-occupied with doing the best thing for the country but with doing the best thing for themselves. All those speeches you can give, on both sides, about immigration!
This is one of the areas where it may be easier to game - at least until the people committing the fraud have gained a bit, shut down the business, and moved on (at least for the smaller instances - larger consultancies would have more difficulty but they game in other ways).
Government agencies are notoriously siloed and often have laws preventing all but the most limited data exchange between agencies.
Consider https://krebsonsecurity.com/2017/03/student-aid-tool-held-ke...
The IRS Data Retrieval Tool isn't "send data from IRS to DoEd" but rather "send data to the individual who then sends it to DoEd".
The exchange of data between agencies is specified in Information Exchange Agreement
https://www.cms.gov/about-cms/information-systems/privacy/da...
https://www.ssa.gov/dataexchange/documents/IEA(F)%20State%20...
https://home.treasury.gov/policy-issues/tax-policy/tax-infor...
https://www.hhs.gov/guidance/sites/default/files/hhs-guidanc...
The referenced privacy act: https://home.treasury.gov/footer/privacy-act
This leads to it being easier for each department to establish its own set of data (so it doesn't need to go through the difficulty of having an IEA with all of that additional bureaucracy and since there's more than enough work for for underfunded agencies working with data that you don't have gets deprioritized) ... and such fraud is likely easier to do or takes many years to raise up enough discrepancies to merit further investigation by qualified investigators.
There is no way to raise the wages of a teacher or for that matter, a civil engineer (https://h1bdata.info/index.php?em=&job=civil+engineer&city=&...) to that of a software developer and have that organization remain competitive or within budget.
Saying "raise the wages in those industries" is equivalent to "let's raise salaries of a school district by 20x and raise the corresponding taxes to compensate."
The issue is that high tech software development compensation is disproportionately high because the corresponding revenue for those companies is likewise high. This is only an issue if you are trying to say that other industries should match it or are competing based on the same scale. I do not begrudge high tech their revenue and compensation, but rather believe that if we paid everyone with a college degree where a H1-B could be employed 250,000 / year that it would cause even greater problems.