"It seems to me right now that idols leave after some unspecified period of time and I don't know why or get any input in it. Seems as if it'd be more complex in real life."
I know AKB and Sakamichi work like part-time jobs, they're free to leave at any time if they give notice. But the most popular girls generally need to wrap up their commitments before leaving and are asked to stay (AkiP haggled to postpone many of the 1st Gen AKB girls' graduations, but let Sasshi leave the first time she asked, for example.). But I see what you're hinting at, graduations are usually things that have to be approved/negotiated with management and might follow the end of their contracts/another single release. I'd also like to see some "haggling" (Although this would mean giving individual idols and their fans more worth so it's actually beneficial to keep girls, like you said.).
I do know the latest update apparently allowed you to convince girls to stay somehow, admittedly I haven't gotten enough graduations yet to run into this.
I think election drama sounds really interesting! There's been drama in the past like announcing a secret relationship, snafus where members shaded other idols, surprise graduation announcements: could be fun.