Asking why you need to use dead wood to create a tanuki bonsai is kind of like asking why you need to use thread from a cotton plant to make a cotton towel - the use of dead wood is what defines a tanuki.Tanuki Bonsai - Cheating or Not?

While some bonsai people don’t consider tanuki a legitimate form of bonsai (because the living tree is grafted/trained onto the piece of wood, rather than the dead wood being an actual part of the tree,) others believe the art can be just as deep as any other bonsai, representing the idea of the phoenix - that new life can come from the remains of the old life. Creating A Tanuki Bonsai - Bonsai Learning Center

There are also several bonsai styes that incorporate the dead wood of the tree as part of the composition. Deadwood bonsai techniques - Wikipedia

Of course you can use rocks and stones. You might use small ones as part of the effect of a tanuki. However, there are other forms of bonsai in which the tree is growing on or around a stone - seki-joju, or ishisuki. Top 8: Stunning Rock Bonsai trees

I would recommend for the best results you either build your own bonsai soil mimicking a bonsai soil recipe from online, or buy a pre-made bonsai soil. It's best to do research of the type of plant species your bonsai is. You can customize the soil a little bit to that species. Most bonsai soil I've seen tends to be very gritty. This gives great aeration and allows the water to pass through the substrate easily. This will allow the roots to thrive. Root pruning is essential with bonsai, the gritty soil particles leave room for healthy root growth. Regular potting soil has too much organic materials.

Here is a really excellent resource for bonsai soil information.

Bonsai soil, recommended substrate mixtures