Agreed on the Home Ec. idea. But, that's not particularly germane to the discussion as it has evolved, or to the video.
The other aside: Teaching physics alongside calculus is the right way to do it. There is a reason that Newton (and others, yes) invented calculus: PHYSICS. Or, more to the point, to understand the natural world. We have split up the whole idea upon which basically ALL math and science rests; applicability to the natural world. Nowadays, we could abstract that to the "real world" by including other extremely practical applications of math, such as economics, even down to personal finance.
Now, back to the point of the video. The president doesn't have much to do with HS science courses, but the maker of the video was brilliant in addressing it to him; we're talking about it, but I bet if it was "An Open Letter to Secondary Education Majors Who Pretend to Understand Math and Science" it would not generate as much buzz, or as much meaningful discussion. So, what change is the maker of the video trying to affect? The answer is much, much, much, much simpler than reworking the foundations of the US education system (different discussion) or even how math is taught in schools. Math sidetracked the discussion, and should be a moot point; HS students simply can't have the math knowledge required for truly advanced physics. Nor should they. HS students should be exposed to the concepts. That is all. They need only a basic causal understanding of physical phenomena to know their world better. And for those who are uncommonly curious, exposure prompts further exploration.
By way of analogy, I am willing to bet that everyone here understands the basic role DNA plays in the world, more specifically in you. That does not mean you understand the mechanism by which genetic information is encoded, much less how the code is translated into macro-level features. But you DO know about DNA, and it is (probably) important that you do. That's all the video was getting at, and I agree with it.