If h1bs are statistically a lot more centered in higher income urban areas, while overall populations of a given profession are more evenly distributed across the country...

Then that $120,000 salary median can still represent a 50% undercut of similar Urban salaries for a profession.

I'm going to contend that that is the case. But I don't have time to chase down the statistics

Underpaid or overpaid doesn't really matter.

Sure it's sound to argue that wages would be higher with more constraint supply.

BUT: The network effect of all SWE talent from across the globe moving to the US is also huge.

Probably, you'd have a smaller overall tax base without H1B. Make no mistake most countries would like to keep their H1B expats :)

If you really wanted to grow US supply of engineers, you'd have to start by fixing the education system, making it cheaper, and then wait 5 years.