What I appreciate about C in particular is that it seems harder to "program by accident" than it is in most languages. C was my first language. After I learned C, I programmed in a higher level language for a while later before discovering that its runtime threw exceptions on 'array subscript out of bounds.' I discovered it by looking over someone else's shoulder in a lab. I realized then that I had just learned not to do that because C was so unforgiving.
We can argue whether the kind of discipline of thought that you gain from that experience is good or even useful today, but I suspect it is. It's different from learning how to do mental math in a world full of calculators - that's just raw mental exercise.