Precisely, because the Rinnegan uses both at once.
Now, thats not saying that a Rinnegan user can't use a powerful genjutsu. They can, but not directly through the eyes. Maybe through sound or hand seals, like Infinite Darkness by Hashirama or Tayuya's flute.
How exactly did you come the conclusion that powerful yin chakra is necessary for genjutsu? Also what jutsu requires powerful yang chakra?
To me it seems you're using circular logic.