I don't see how anyone could be "awesome at CS" without being strong at math. Being skilled at *programming* and bad at math? Sure, although that would be a significant handicap.
Programming isn't CS, just like machining isn't mechanical engineering. Sure, machinists and mechanical engineers tend to have a basic seat-of-the-pants understanding of each others' disciplines, but that doesn't mean they can do each others' jobs.
Of course CS is different, in that many if not most people with CS degrees make their livings as programmers. And probably quite a few of them are mediocre at math in a way no mechanical engineer would be, but I wouldn't call those people "awesome at CS"; I'd call them over-credentialed programmers. On the flip side there are programmers without degrees in CS who are awesome at CS, but that's because they've self-taught, and are pretty much by definition good at math. They may have deficits in specific areas like geometry or calculus, but they're going to be good at stuff like abstract algebra and graph theory. If someone is "awesome at CS" they should be able to follow Euler's solution to the Konigsberg bridge problem. If they can't follow it they may be quite useful as programmers but they're not going to be designing any novel networking algorithms.
As far as making CS a core subject? That seems a bit extreme to me, and I actually have a CS degree. I think most people who are destined for STEM careers would benefit from some programming experience in something like MATLAB, but they'd benefit *more* from additional probability and statistics. There is certainly little call to teach them actual CS. It's questionable to me whether people heading into non-STEM careers benefit at all from CS or programming, and they'd certainly benefit more from additional courses in writing.