Apologies if my original reply made it seem like it can't.
Why don't teaching systems in America incorporate both the majority of the time?
Two major reasons:
1. Cultural inertia. Most teachers emulate the pedagogy that they experienced in their schooling. Some are aware that you can try to mix conceptual+procedural and try to. I call them the "notch generation"- trying to teach in a way that is different than they were taught. It's hard to do because...
2. The system is not designed to accommodate it. Incentives and higher order effects all conspire with cultural inertia to thwart it.
I've worked in both K-12 and post-secondary education, studied the history of education reform in the United States, and visited schools/met teachers/students/etc that I've connected with across the U.S.
I'm always interested in hearing someone's story about school, how it did/didn't meet their needs, and how it has impacted them.