"It would make sense that an employer would try to offer a lower salary to an employee it helped move to the United States since that employee also gains the benefit of getting sponsored, but the analysis found the opposite." This makes me want to punch the screen. It is ILLEGAL to pay an engineer on an H-1B less than the median salary for that position, precisely because people were worried that foreign labour would…
By 'that position' do you mean the position being replaced, or the new position created in order to hire the H1B? And are you taking account of the market price of the additional skills that employee brings, or is that not relevant?
So here's just one loophole: companies find a lower-paid title, and base the 'prevailing wage' on beginning level employees. Now that the 'prevailing wage' is set, try to hire young people with advanced education, special skills, etc. Congratulations, you now have a legal way of paying about half of what a comparably experienced citizen would cost. Bonus: sponsorship does provide good leverage.
Consider H1B employees getting paid the prevailing wage. Is this how you compensate the best talent during a talent shortage? No. It implies you'd pay less if you were confident you could get away with it.
You can't honestly dispute that the program is being used to undercut wages. Legally.