For now the attributes have two functions: Increase the amount of money money you earn by working or to create some variations in the story.
Story progression will never be limited by attributes. They are a bonus for other secondary things. The grind is optional and not mandatory (Costumes or Gifts do not affect the story).
There will be more content that needs attributes in the future, but it will be secondary content. This is something that I have deliberately put off during development, because first I want to add things that I consider more important