Can anyone think of the reasons why the defense would want this person identified.
The reason is simple... The SANE nurse is a material witness, whose identity is currently unknown to the defense. This individual's conclusions have been used to justify this witch hunt, but the person is not now subject to questioning.
If the prosecution wants to have this nurse as an "expert witness", then the defense gets to know who they are - if only because the person's identity will reveal the experience and expertise they do or do not hold.