By this point you're probably sick of us pointing this out, but once more, all together now: "The studio is a metaphor for the woman's relationship!" Every aspect of the studio in "Living in Sin" can be read in a way that metaphorically also describes the relationship.
Dirty dishes, shmirty shmishes. Even if this studio were sparkling clean, that wouldn't change the problems in the relationship at all. It would just cover them up.
A good clean may be all she needs. If the woman wants to fix her situation, she should start by confronting the dirt around her, instead of trying to ignore it.