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> one option is to list occupations that are in short supply each year and to prioritize those

That's a lot of what prioritizing slots by pay does: pay is higher for jobs with low supply relative to demand.

I suspect that the real problem with prioritizing by pay is that it shows that a lot of employers are using H1-B workers to put downward pressure on wages.

Also there are a lot of parties involved in gaming the complex system whose services wouldn't be needed if the solution was that simple. I think Upton Sinclair's quote applies here. https://www.goodreads.com/quotes/21810-it-is-difficult-to-ge...

Not necessarily. You need farmers and scientists. Can't do a descending sort by salary.
Wasn't Trump's proposal few years ago "95th percentile salary for their profession"? So you still have room for farmers and scientists provided that they are exceptional (or at least exceptionally well paid) farmers and scientists.
The executive can't do anything. It has to be passed by Congress. Congress hasn't passed anything in 30+ years.