If H1B immigrants generates more tax revenue and contribute more on average than locals, largely because of gems like Sundar Pichai that couldn't make the bureaucratic credentialist hurdle of the O1, then what's the problem? It should be expanded and reformed, not contracted and reformed. If you're concerned about degree mills then reform that aspect while expanding the net intake.
Iād be fine if a third of the total compensation was diverted to a fund that all but takes a minimum of 50k per person per job /gives 100k minimum tax-free per affected citizen in the lowest LCOL, both adjusted upward for locality. To make people whole, that fund would cover citizens in the job market from 2003 onwards that specialized in anything with exposure to the various programs that disincentivized citizens. Then have it apply irrespective of job status.
If you want the best and brightest, pay for the damages created by badly formed policy.