One of the flaws of common core is that it seems that the proponents did a poor job of marketing it to the broader adult community. Doing so would have:
1) Given parents the answer to "why is this change happening at all? I learned math just fine as a kid!"
2) Engaged some people in trying to think about the best ways to explain that material and accelerated the formation of a community that gains status with each other by coming up with better and better explanations of the common core curriculum.
Computational skill is used as a proxy for understanding because educators, just like the rest of us, are lazy-ass human beings. The authors of standardized tests don't care if you know what an eigenvalue is, only that you can calculate one.
Or, put more charitably: teaching math is hard as hell.
Like so many other aspects of our lives, modern math education in the US grew out of a knee-jerk response to a perceived crisis -- the launch of Sputnik, in this case -- that wasn't very well thought out. Schools were required to measure kids' progress in math and science quantitatively, precisely, and repeatably. And just as in other fields, once a measurement becomes a target, it ceases to be a good measurement.
The videos also make me angry because it frustrates me that such explanations were not available to me earlier in my life. What is it about the state of math education that this kind of explanation is not there in every class?