I guess they'll just have to settle for (horrors!) American workers.

Meh. If H1B were reshaped to actually be for specialist workers as it was intended (at least by some), then that's a lot easier said than done. I got to the US on a temporary work visa (not H1B because of loosing the lottery), and I'd find positions for somebody with my and a bunch of other specializations several times over.

By auctioning based on salary you're preferring areas with absurd costs of living - which is a) not where you necessarily need to get more people making the problem worse b) reinforcing economic inequality between areas of the country.

If there's a company needing some specialist somewhere with a saner cost of living, and they tried to find such a specialist, offering above market wages, what exactly is the benefit of not them having to pay twice or thrice the effective salary of somebody in SF/NYC?

You can always adjust salaries for cost of living in the area to have a more apples to apples comparison.