They already are.
> not be tied to a specific job
I agree, and lobbied for that on the Hill years ago but this was during the DREAM act battle [0] so it got nowhere.
> you’ll simultaneously boost the supply of highly-skilled workers and ensure they get a fair market price
I agree.
[0] - https://www.politico.com/story/2013/12/nancy-pelosi-immigrat...
More American consumers would be negatively impacted by layoffs in well paid manufacturing industries that are fairly geographically distributed like the automotive industry than an industry that is consolidated in a handful of single party states like the software industry.
More bluntly, SWEs primarily live in single-party states like California, Washington, NY, and Texas; represent a fraction of employees Americans; and work in a politically irrelevant industry (if the tech industry was actually politically powerful the H1B rule would have never been proposed). In essence American SWEs are politically irrelevant and do not matter as they cannot swing elections.
[0] - https://www.bls.gov/oes/2023/may/oes151299.htm#nat
[1] - https://www.bls.gov/iag/tgs/iagauto.htm#emp_national