I see lots of good ideas about changing the selection process. Another option is to change is to change the new hire process and require employers to advertise every recent H1B hiring decision for 60 days, including job description and resume. Then a native with an equal or better resume, and a willingness to fill the role, can raise their hand and offer to replace that person. If a native with a better resume is denied, then it is a cause for action against the employer (ideally a fine paid to the applicant that would at least fund further search time). Repeated violations would result in wholesale revocation of H1B access.