1. Mixing
Currently I find most bass lines barely audible, but there seems to be no way to change the volume of each instrument. Being able to do that would imo improve the lot the song writing part.
In addition mixing may allow to integrate more the song writing part into the main game if it actually impacted band performance (to resume setting one musician volume higher than others should make him matter more in band score and so would be a good idea if you have a far better musician for one position, but would create conflicts with other band members).

2. Mouse over popups
Instead of having to click a musician and then manage member, a popup on mouse over showing his skills and relations would be far more practical.

3. Improving calendar and making it more accessible
If I haven't missed something there are just two ways to access calendar : the top bar where you only see the next week and clicking on map then on a city then on a place and setting a date.
A calendar icon allowing to access the full calendar from main screen would be a good idea.
In addition the popup on dates can be improved and show the list of songs you are going to play in each place. It's important to be able to verify that due to the song selling event. As I rotated my new and old songs to slow their novelety loss I ended a few times selling songs I was still going to play and having dates cancelled due to that.

4. More life out of the group for band members
I find human management is currently the poorest part of the game, band members having no family obligations, passtimes or vices (except if you take a drug addict), commitments like having a "real" job (even for the musician having this trait).
It would add a lot to management (and difficulty) if they had, and at least occasionnally demanded time off to deal with their lives (you can then accept and have the member unavailable for a while or refuse and see tension rise).
Ideally you would need to have access to temporary replacements for this to work without being too punitive (if one musician is unavailable for some dates you'd have to recruit a temporary band member for the date not to be cancelled - it would actually make the "recruit member" part more useful as actually you use it one or two times in the beginning then never again as it's easy to max cohesion and raise skills), or a system where you can play with 3/4 band members getting a reduced score.

5. Renaming samples in song writing
Re-listening a dozen of samples to find that 7a or 11c is the one you were searching can be a bit tiring if you don't have a good memory of obscure codes. Allowing the player to rename samples and say call 7a "melancholic ballad" or 11c "noisy metal" would be a good little improvement to song writing part.

6. Improving/developping clips and albums design
Ideally clips would need a completely different system/minigame than just playing the song (except if you make totally unoriginal clips where you are just playing).
Being able to chose what kind of clips you make (eventually with different costs and pleasing different local publics) would add to ambiance and management.
As well for album designs, chosing a cover between several themes pleasing different local audiences would be a good idea (and having to pay graphists to make them).