These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Family-Unfriendly Aesop: In regards to Amane's entrance into the Etoile elections, the moral is "It doesn't matter what you want, it matters what everyone else wants." This might overlap with Values Dissonance - placing aside your own wants in favour of helping the collective is a prime example of Japanese social mores.
Kaname even subtly lampshades it with her actions, being the "evil" counterpart to Amane. She wants the position of Etoile because she wants the responsibility and has plans she wants to accomplish, whereas Amane has no desire to do so, despite many believing her qualified for the position, and confused/disappointed she wouldn't assume duties she is believed suitable for.
In the end of both the anime and the light novels, however, Amane is very happy in her new position. The light novel ending explores this further, as Amane is glad to accept her role as the new Etoile as a way to bring happiness to not just Hikari, but all of Spica, and states that "it feels good to be needed by someone".
Fan-Preferred Couple: Some fans would have preferred Tamao and Nagisa to end up together. There are quite a few fans who feel the same way about Hikari and Yaya.