Adding on to what you're saying: I think it's pretty clear that Morrowind and Oblivion are more focused on a first-person perspective for the player character with third-person being a bit of a secondary concern. As such, it seems to me like the focus of the third person animations is on matching what the player would see in first person, especially since they can switch between the two with a single button press.

For example, when the player holds the "A" key to move pure left while keeping their view straight, it certainly seems more natural from a first-person perspective that they're strafing left rather than turning their torso left with their head and arms awkwardly straining at a 90° angle (try this at home, it feels weird).

The alternative here would be for the character to actually turn their whole body left when you hold the "A" key in third-person, but then have their view (i.e. their head and arms) snap 90° to the right whenever you switch back to first-person, which seems odd and immersion breaking.

That being said, obviously it does look quite jank from a third-person perspective for a player to be strafing all the time, even when they're in non-combat scenarios. This isn't helped by aging animations, either.