>Most introductory courses these days focus on trying to teach students to understand how to solve problems (usually to some degree agnostic of language) and then how to turn their solution into code.

The "to some degree agnostic of language" part has been available for a long time in computers, initially as flowcharts and later as pseudocode.

>and b) has the right mindset to properly frame their ideas at the low level c operates at, C could be a good starting language

That requires prior knowledge and practice more than a mindset, IMO.