Why do you think the Tenseiga couldn't save Kagura?

When Sesshomaru finds Kagura dying from the Miasma he reaches for the Tenseiga but then stops himself and says Tenseiga cannot save her.

Is this because she doesn't have any actual soul of her own? Since she's only an incarnation of Naraku?

Or is it because her true wish was to be set free and become "the wind"? She didn't want to go on living.

Why do you think he wanted to save her? Do you think he had sentimental feelings for her, romantic or otherwise?

One of the saddest deaths. Poor Kagura.