Not really, Big Tech pays H1Bs competitive salaries (https://insights.dice.com/2020/05/19/google-apple-amazon-oth...). What this mostly affects is IT consulting firms like Tata and Infosys.
That doesn't challenge the argument. Wages are set by supply and demand, expand the supply and wages fall. It doesn't matter if H1B wages are similar to a U.S. residents; wages as a whole are depressed.
As a personal example, the entry level of my field is almost completely composed of freshly graduated H1B Visa holders. The market rate is dictated by whatever their wages are, which actually isn't too far below the $200K headline number.
On the other hand, the H1Bs working at big tech with higher salaries are more likely to later start another company, which will increase demand for top tier engineers, but this effect will take longer to materialize.
But ya, we don’t need to import someone doing JavaScript over to America anymore (which, believe it or not, is what I’ve witnessed). There’s no rhyme or reason to it, we have a solid home grown talent pool for that.
A lot of full stack web dev work can be saturated by Americans because there’s enough people crossing industries to take it on.
I’ll let the other types of developers chime in on what kind of shortage they are seeing, because I see zero in web development. It’s nothing personal to my immigrant friends, but believe it or not our industry is pretty crowded at the moment to justify opening up to foreign workers. We can easily drive prices down amongst ourselves at the rate we’re going at.
I support this policy through and through, and I’m a Democrat.
Being able to program language X isn't really the marketable skillset at the high level. You don't hire good javascript programmers. You hire good programmers