Allow me to share my two cents with you guys. You've brought some really great ideas to the table here, and mentioned some aspects of the game that really could benefit from a few tweaks and changes.
First, we have single sales and data. Though this is relatively minor, it would be incredibly cool to have a menu or a tab dedicated to details stats and data about your singles, groups, employees, everything. From the most obvious 'Total single sales' to stuff like 'Time spent writing lyrics' or 'Failed negotiations'. Again, it wouldn't be the end of the world if that feature doesn't make into the game, but it would be nice being able to take a look at everything you've done while managing your company. Additionally, adding continuous single sales to the game would be a nice little touch of realism indeed, even though it could affect the game's economy (negatively, in my opinion), so it would sure be welcome.
Now, about idols and levels. I completely agree with what's been said about getting attached to the idols we start the game with and not wanting to replace them with other idols with higher attributes, though, at the same time, I also understand those who would rather have an ultra talented team of idols they barely know instead of a team of average idols that have been with you since the very beginning. I guess the choice should be the player's when it comes to that, and no big changes are necessary to the system directly, although I do think IM could draw inspiration from games like FIFA in two ways:
1 - I'm sure you've heard of people who go absolutely crazy when they pull a rare player card on FIFA ultimate team. That's what it should feel like to pull a platinum idol in a "pack opening" (although, without the scummy "surprise mechanics"-styled microtransactions. Or with them, I don't know. Whatever the fans are willing to pay for a successful playthrough, I guess). Platinum/Gold idols should be rare, probably rares than they currently are, but that's not the only thing;
2 - Besides being rarer, I believe the platinum, gold and silver statuses should be more related to potential than to current attributes. Now, I admit, I haven't played IM in a while, and maybe my memory is failing here, but my food for thought is the following: pulling an incredibly talented idol with high stats in an audition should be ridiculously rare. Just think of all the other idols groups that could snatch her before you can. Maybe the player's influence could play a role in the quality of the idols you get during auditions. Maybe it already does and I'm just late to the party. What I'm trying to say is: it doesn't make a lot of sense for an incredibly talented idol to be a "free agent", and not already be part of another group. Maybe those silver, gold and platinum statuses could, instead of referring to girls who, for some reason, have 93 vocals, but are auditioning for some broke-ass low-tier idol group, refer to prospects - girls who might not have those great skills yet, but have anormous potential. But then again, that's just my opinion, I just figured it would be more fun working on building your idols form the ground by training them instead of having a superstar audition for your group, someone who already has great statuses. Those should be obtainable only by "snatching" them from other groups.
Last, but not least, let's talk about money and success. Getting rich in IM, especially in the hardest difficulty, should be comparable to the real life road to success of a small, new agency. It should be hard, it should take a while, and it should require precise decision making and a lot of effort. We want to fight for it, we wanna feel like we could always be a scandal away from going under, we want the hardships that precede the reward. But we (and by 'we' I mean 'I') don't mind failures. We want the hard difficulty to be... well, hard. Don't be afraid to make the game ruthless, make us go broke and force us to restart over and over again until we get the hang of it, until we manage to at least get out of debt.
The short version: less income, more expenditure, fewer idols with high attributes, more idols with low attributes, grinding, data about your group. :)