Caption styles are lost in translation

While editing content with a WYSIWYG editor, you are able to style the caption to include alignment on the caption itself. But when the node is saved, the alignment seen in the WYSIWYG editor is not there.

Is there any way to preserve the alignment settings that the WYSIWYG editor applies within the [ caption ] tag, so What you see can be what you get?

To reproduce:
- Add an image to a node, give it a caption.
- Use the insert module to insert it into the body.
- Highlight the caption, click "align left" in the WYSIWYG editor
- Save the node.