I never thought of making sure all the sims have one in each music skill, I'll try it, but I don't recall ever having to do that before.
I don't have any mods, but I do have several CC's like clothing, cars and I recently added electric guitar meshes; I don't know if the things I listed count as "mods" but maybe they're part of the problem.
No, clohting and objects don't count as mods (at least for me they don't)
The skill thing is something I came across when googling your issue. I'm not sure if that's the problem.
