Good to see the simplification and the solution of some inconsistencies. Really the status of Bounding Boxes should be reevaluated :)

• API to retrieve a bounding box returns by value to make it clear there is no caching and to simplify code.

This approach is a bit strange, especially since the BoundBox struct isn't that small (8 x 3 x float + bool + pad).
Another option would be to pass the reference as a pointer as an *r_bb arg.
I think passing it by reference makes it clearer that the BoundBox is a struct and not a simple type.
But that's not really a problem.

Also on style, I noticed that some "_get" suffixes suggest, at least to me, that the boundbox is cached (which is not the case for example with BKE_armature_boundbox_get). Maybe it's more convenient to rename to "_calc"?

Also I fear that the lack of boundbox caching support in some types might impact the performance of some modal operators like the transform whose snapping reads the boundboxes of all objects in the scene.
For simplicity, in order to avoid creating a new flag for each type, perhaps we could indicate that only the boundbox of the object is cached. And avoid calling functions like BKE_armature_boundbox_get?
(Or everything could be cached).

Anyway the patch is still WIP, maybe it's too early for these suggestions.

(Also I think the bool valid member of the struct BoundBox is out of place).