The Rabbenu Bachya explains that nefilas apayim is smilar to puting the feet together at s’e showing tnat without the help of Hashem we cannot move and our body is tied up as our feet.
After the death of Korach and his assembly, a mageifa breaks out among the Bnei Yisroel. We see that Aharon is told by Moshe Rabbeinu to go amongst them and offer ketores in order to be m’chaper them and thereby stop the mageifa. IY”H, in a few weeks, we will come to Parshas Balak where we see Zimri take Cozbi and sin in front of Moshe and the Klal. When a mageifa breaks out amongst Shevet Shimon, Pinchas comes and kills Zimri and the woman, and the mageifa is stopped. It would seem from these two incidents that the koach to stop a mageifa is given over to the Kohanim. While all of our tefillos are obviously necessary and important, in this particular nisayon, those of the Kohanim should clearly be loudest and strongest.
The Kohanim are diligent. The closer we are to Hashem, the more we can accomplish. The rebbies daven for others. Aharon Hakohen was second to Moshe Rabbenu at Mount Sinai but Korach was out for himself and his argument being kohen gadol was illogical. He never explained what makes him better than anyone else. When a person has self interest, he does not lthink logically. The Ben Ish Chai says לא יקרחו קרחה בראשם do not tear in what is infront of you. Before כהן before ‘כ’ is ‘י’ and ‘ה’ is ‘ד’ and ‘ן’ is ‘מ’ making מיד diligence.