I had exactly the same experience - it felt like the "D Dorian is C major just starting on D" was a back-to-front way of explaining it. As you say, thinking of D dorian in relation to other D scales, especially the D minor scales made so much more sense. I did learn them for my double bass teacher, but Dorian is the only mode I've actually used.
Edit: this has been rattling around in my head since Sunday, and ended up writing out some scales and modes. It puzzles me that dorian clearly fits into the 3 minor scales, but is taught very differently.