Yui's submissiveness is only that strong in a sexual context. Outside of it she is capable of reining in Aki if necessary. It's not really her main job, though. She's more of an aide and best friend, which, of course, includes stopping Aki if she's about to do stupid things.
Thinking about Yui's.. personality is not a bad way to distract yourself from IRL things. Could do a lot worse. :P
On completely unrelated note, some bug-report like things: