This is a very well known issue that has been brought up before. The NYT Piece has a basic error: the case highlighted of Mr. Négri - His H1-B Visa was not Denied (which would imply that his case was processed), it was returned without being accepted.
There are also two well know tweaks that can take the perverse incentives out of the H1-B system:
1) Allow the H1-B to be a work permit with free movement between like jobs at other companies - this will reduce underpayment and remove the virtual slave-labor conditions of an H1-B holder
2)Reform the Labor Certification process (the precursor allowing you file) so that it actually ensures that no Americans can be found - the current state of the LC system is a joke.
I am not sure how you can reform the labor certification process when the goal of the process is to find 'whether there are qualified Americans' to do this job.
Other than a very few cases, I guarantee you that there is not a single job where you can't find an American to do the job if you are willing to pay the price.
There are also two well know tweaks that can take the perverse incentives out of the H1-B system:
1) Allow the H1-B to be a work permit with free movement between like jobs at other companies - this will reduce underpayment and remove the virtual slave-labor conditions of an H1-B holder
2)Reform the Labor Certification process (the precursor allowing you file) so that it actually ensures that no Americans can be found - the current state of the LC system is a joke.