Remember, H1B isn’t always about tech, even if we’d all like to pretend it is. You’ll have to have separate bidding process for different occupations, otherwise you’ll end up with a system where Facebook will get all the visas, while in some cases, doctors would not be sponsored.
There are plenty of jobs as a doctor that pay 350k+/yr that are vacant and are being filled by H1Bs. This mostly is in areas that have low cost of living. You could literally buy a good house with that salary within a year and fully pay for it in two. But people just don’t want to live or work there. Even doctors would prefer to be in NYC or LA over Jackson, Mississippi.
I'm curious what makes you think tech workers would monopolize the top spots? I would expect that companies desperate for experts in medicine, research, engineering, law, business (which, like tech, already pay high salaries) would be similarly willing to pay a premium to be able to hire the best from other countries.