Stars like the Sun don’t have Star Seeds; only the celestial objects that orbit them do. That is why they are called “star seeds”.
It is too much for one senshi to have the fate of her entire solar system in her own hands, even if she had aid. Perhaps long ago this was the case, and this is why senshi who bear names of the star do so — even though their star seed belongs to their planet, they honor their predecessors by carrying their title.
