So H1Bs would end up only working in NYC, Bay Area etc and only for the big players. Not good either.
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?