While I agree that different plants have different requirements, to answer your question about clay-based rooting medium... I'd always heard to use sand.
Many plants will root in sand without any special treatment.
Other plants require special times, special hormones, bottom heat... And, still may not root.
So, what are you trying to root?
This spring, I've been taking cuttings of various climbing roses, and rosemarry. They seem to be growing, just by potting in sand and leaving in the shade.