You make it seem as if there is a large pool of engineers that operate at such levels. Even in something as mundane as "business management", the best players will be fought over. Now In the business of intelligence and mathematical algorithms, it's not 'gutso' or 'drive' that we seek, it's ability and a large number of American engineers simply don't know, or care about 'boring mathematics'.
You're promoting that companies "aren't paying enough". Maybe for IT work as that becomes the new 'mechanic' commodity. As far as hard mathematics, there has always been a shortage of qualified workers and we can't keep fighting over the same number of engineers as it's just musical chairs. Your solution is gating such that 'eventually' graduates will be incentivised to do the hard math required, but I can tell you that we have been offering 150, 200k+ salaries for the appropriate experience. Now if you want fresh graduates, that's 80 or 90k which we offer to both foreign and domestic applicants. Same fresh faces, one side having a mathematical edge, why should I hire someone who clearly doesn't know what they're doing as opposed to another who has a great mathematical grasp and can learn the rest.