I like the idea of an auction, but why would we not charge a significant application fee? It ensures the company is serious about the position, and it raises money citizens won't have to pay. A high fee/tax seems like a win-win
This insures that tech and finance get all the visas. A lot of things like rural medicine gets staffing through h1b sponsored physicians and likewise for post-docs and researchers. If this gets implemented across the board, a lot of science is going to disappear and a lot of medical care (especially outside of cities) is going to get a lot worse.
This has been proposed before and I don't really see any downsides. If your company really needs them, just pay them what they're actually worth.