Yeah, it's really amusing that anyone expects anything innovation-wise out of the US when we basically put the minimum amount of money humanly possible towards education (for the majority of the country). Looking at Asia and the Nordic countries and how highly they value educators, it's clear where all the talent is going to be in the coming decades.
And when you look at tertiary education, the amounts we spend are shocking.
Education in the U.S., like healthcare, and even defense, is an example of spending way too much money for the quality of the outcome. For a variety of reasons, we have little public capacity to efficiently provide government services compared to what the rest of the world does. This is even true for things like public works spending.
Anyone that tells you we are "not spending enough" has either no idea how much less the rest of the world spends, or they are just lying to you (usually it's the former).
Just because Khan Academy teaches it doesn't mean it's the most effective, most useful, or even correct method. They too are victims of needing money. Teaching what is currently being taught has been their bread and butter since the early days.
I can only speak from examples I've seen from young ones in my family "acing" early math and suddenly struggling with trivial stuff like Geometry, more advanced fractions, factoring, etc.
Common tricks like so-called "number bonds", "colored numbers", excessively complicated math for simple arithmetic by using shapes, preferring "regrouping" to carrying, etc.
All of these are valid, and with the correct level of sophistication a student can learn these tricks fast and use them correctly. The issue is you're dealing with kids who haven't gotten any sophistication yet. The reason things are initially taught rote is not because of some shibboleth of mathematics but rather mathematics can be useful without always knowing exactly why something works. There are some examples of common core problems floating around the internet that border on introductory number theory. The premise of it is ridiculous. Your child arrives to high school or college with a cobbled together book of poorly learned tricks that end up having profound influence over their ability to digest actual complicated math.
To drive the point home a "common core" version of calculus would have you learning real analysis long before you even understood a derivative. It's asinine.