Now its their turn to take care of things (house work and nursing Yuu)... and maybe successfully failing in that, which I'm pretty sure will make the sisters realize even more how important is Yuu in their lives. And maybe down the road will make for a nice base for an arc about Yuu's inferiority complex (If that ever happens).
...with how incompetent they generally are at housework, they're more likely to prolong his illness. Which is exactly what they're after: To make him hopelessly dependent on them instead of their chief rival, their own father.