Kson was actually pretty clear, as Coco, about the reasons. She can't sing, doesn't like singing and it required a lot of time/effort. And she felt horribly inferior about it. Which might also been the fact she was living with Kanata, a Singing Otaku. Kanata's autism about singing craft might have driven Kson out.
Realistically, though, Coco had run her course. Kson wasn't that interested in being Coco, she was completely in here own head about the character and was simply ready to move on. Cover did want her to stay, the rrats about silently booting her never made much sense. I can see some lower management giving her the cold shoulder in standard Japanese Office Culture, but Cover gave up China (and still gives up China) for her. Granted, that's also the better business decision in general.