I worked at the state unemployment office for 15 years and we’d regularly get job orders doing just that, since it’s the law. Now maybe that has changed since I left, but I doubt it. Employers DO have to go through a procedure to make sure there are no qualified Americans. Some of them, of course, would write the position in such a way as to make sure there were no Americans that could qualify (proficient on the XYZ machine and speaks fluent Mandarin) but they did have to allow a search for a qualified US worker.
Whatever the rules may be for companies paying people to work on something they do for the government, there are plenty of jobs that are never advertised in the US and are then filled with people from overseas.
Employers DO have to go through a procedure to make sure there are no qualified Americans.
It’s plainly not effective enough, and the recent abuses of the H-1B visa program by companies in California which fired Americans to replace them with people hired on H-1B visas show that standing to sue is needed. Adding an extraneous Mandarin fluency requirement for a position which does not involve work in China ought to be the basis for the company losing such a suit.