There actually
IS exactly such a requirement to advertise positions in the US and accept applicants. The issue is that it is gamed or done only perfunctorily. What you are looking for is enforcement, which costs money, and goes against the desires of the companies lobbying for such legislation.
It would also help enormously if the immigration was not tied to a specific company, i.e., the worker could jump to a new company at will without having to convince Company-B to do the whole sponsorship process. As it is, (iirc) if they lose their job, they have only 90?180 days to find a new sponsor or go home. This would make it much less exploitative, and also lower incentives for companies to sponsor H1Bs instead of seeking US workers. Write your congress-reps & Senators.
(Source: tech co founder in some companies that did H1Bs, so not sponsoring but managing the workers brought under the process; also competed under a coach that my school took exceptional efforts to get here from Austria because of his world-class qualifications, they still had to really fine-tune the requirements)