I'm not a yank but it seems to me the actual argument here is that H1Bs suppress the wages of locals, either directly by hiring foreigners which are less price-

I'm not a yank but it seems to me the actual argument here is that H1Bs suppress the wages of locals, either directly by hiring foreigners which are less price-sensitive in terms of wages compared to locals or indirectly by moving jobs overseas, thus eliminating the jobs altogether. You can be pro-immigrant while also being pro-not-fucking-people-over, for example by forcing companies to have a baseline "minimum wage" for H1Bs that match what a local would be paid (or higher!) for the role. It doesn't have to be a "let in a gazillion people or 0", you can choose a middle value.