You could just make it for employment visa based on the employer. (or edu visas based on schools there). In most of those cases you already trust the employer t

You could just make it for employment visa based on the employer. (or edu visas based on schools there). In most of those cases you already trust the employer to some extent, and can rely on audit and heavy penalties to deal with fraud after the fact. You would be doing the important anti-criminal/anti-terrorist screening to a consistent national standard. It wouldn't be the full immigration system -- it would just be nice for states to have some role. There already are incentives to recruit doctors to work in underserved areas.