The more I know about Nanao, the more I realize how charming she is.
To me, Nanao is the personification of a person with a healthy self-esteem. I see people get turned off by her assertiveness. By her assertiveness, people think of her being too pushy, possessive, and whatnot.
But to me, it couldn't be further to the truth. Nanao's assertiveness is not rooted from her possible arrogance that people are below her, nor is it from her thinking that she is the center of the world. No, it's because she understands that she has the right to express her feelings of love and affection to her beloved. And as she says, "Is it really such a bad thing to try your best to get the person you like to notice you?"
There is simply no sense of insecurity or fear of rejection which people often relate themselves to when they are anxious about expressing their love. She simply exercises her rights to say "I love you" to Izumi in what I would argue the healthier way there is.
The fact that she helps Amane is not necessarily because she wants to help her competition because she is too strong, but it's simply because she knows Izumi cares about Amane.
Again and again I say this, Nanao is the kind of girl whom you would want to spend your lifelong partnership with. Well played author for creating such a character.