Kabalah needs a Kohen and therefore needs to be held (in the right hand).

I assume that you are bothered by the Kli from which the Kohen is Kometz, and not the Kli into which he puts the Kometz. Rashi writes that Kemitzah needs three Kohanim, one to hold the first Kli, one to hold the second, and one to be Kometz, and all need to be done with the right hand. The Acharonim question why the first Kli needs to be held. Similarly, they ask why does the Kohen need to hold the bird for Melikah which is what makes the Avodah so difficult, when it should be enough for him to do the actual Melikah with his right hand. The general answer is that every part of the Avodah needs Kehunah and Yemin, and that includes making the Minchah available for Kemitzah.

D. Zupnik