After complete watching anime, I feel that Yui is a wasted great character. She has a lot of potential to be a great character, but every opportunity is wasted.
First, her background and character is inviting a horde of doujinshi with bad intention. The potential is quite malicious.
The show starts with her years as a cadets. She makes friends with her new found classmates. As a typical mecha anime, the main girl has a rival. After several competition, they eventually become friends. This good start is ruined by the end of second episode. T_T Maybe it's expected. As cadets who haven't completed the training, they are outnumbered and outgunned. They already did their best.
Now, move on. About her military career. Her ancestors were royal guard and samurai for many years. Her father is a high ranking officer. So, it becomes her duty to take over her family business. She has to shoulder the burden of her family's pride.
The politic is in her world is quite dirty, not saying the real world politic is clean. It's why she does not trust foreign countryman(a dirty doujinshi material). In her world, JPN empire military didn't surrender and disband. It's similar another fantasy show, Striker Witch. However, her military still acts as vassal of a foreign military. She cannot trust that faction. She believes that faction is planning world dominance. So, it's waiting Euro-Asia to be wasted by Beta. Yui knows that she still needs that country's resource assistance. Yui also distrust another superpower. Her country asks another faction's collaboration through UN. That faction also seeks world domination. That's why her empire military didn't ask for that superpower's assistance during Beta's Japan invasion. It may leads to the occupation of Japan.
Neverthelss, she still respects the ace pilot from that superpower. In the promotional video, she calls that pilot as her enemy and comrade in war field. She also claims that person is also her rival in love.
As a potential harem anime, Yui falls for the main guy for no reason. Maybe there is a reason, but it is kind weak. His passion in winning may be intriguing to Yui. Yui wants her project to be successful. So, Yui's trial starts as fighting Beta. Then, it becomes resort type training in Alaska. She even provides the fan service at beach and hotspring. Then, she has to engage the humanity's internal conflict. It's no wonder some people think the write hate the countries in real life. So, the writer screwed up the romance and plot.
Since the series is only a subplot, Yui's character development stops suddenly. Too bad, Yui's character development still has potential.