On my wiki, I used to include all parent categories in the list of categories at the bottom of each page. For example, for a page named "Dachshund", in addition to the "Dog" category, I would also put the "Mammal" and "Animal" categories. Same for category pages, so on the "Dog" category page, I would assign it the "Mammal" and "Animal" categories, etc. I did it this way because I felt that when someone lists all members of the "Animal" category, they should see the subcategories and their pages as well. But that means you end up with a category tree like this:
Animal
+ Dog
+ Dachshund
+ Mammal
+ Dog
+ Dachshund
+ Dachshund
+ Dachshund
This bothered me, so I made a patched version of the CategoryTree code that produces a tree like this:
Animal
+ Mammal
+ Dog
+ Dachshund
But then I decided it wasn't worth the effort updating the patch for new MW releases, so I switched back to regular CategoryTree and I don't include parents, grandparents, etc. in categories and pages on my wiki anymore. Anyway, I just wanted to share my thoughts and experience.