Reduce kd-tree's nodes' bounding box sizes to their shapes' extents?
No disadvantage that I can see but what you have is not a kd-tree if you have axis-aligned bounding boxes in every node.

A kd-tree only has a splitting plane in every node, so there is no AABB to shrink. The way to deal with empty space in them is to split the node further into an empty node and a smaller node with the same objects as its parent, when justified by whatever heuristic is used. It is just one more possible split to consider when picking how to split a node.