We already have a system for that -- taxes. Why would you underpay H1B workers? It seems punitive w/o cause.
1. It is unfair to the workers
2. The H1B Programme is for top talent, for talent you cannot find locally. If anything you should overpay for such valuable talent.
3. High H1B salaries also come back to the country in the form of taxes just like for all workers, which should improve schools.
Schooling is a shared problem for communities and our country, and should be paid for with taxes -- why would you put the burden of that on immigrant workers?
Finally, if despite taxes, we cannot fix our school system, perhaps instead of blaming/punishing immigrants we should be looking at our municipal and state governments.