Some games do, some games don’t. It’s a design choice.

Also, Oblivion was released originally in 2007, and Morrowind in 2002. The consoles, game logic, and gfx were a fraction of what modern games can do, a lot of games (most, in fact) back then didn’t have the fancy animations for all directions. There were likely other backend/engine limitations at the time that don’t exist today, because CPU/GPU power.

ETA: as someone who has coded a 3rd person camera and animations in 3D to work in all directions, it really fucking sucks to do in a well-known engine with online search available from others that have done it before. Now imagine having to code everything like that from scratch into a custom game engine, being one of the firsts to figure it out. I’m also gonna guess other bugs were far more important than which direction the character is walking in TPV, being a Bethesda game and all.