From my understanding the Elites were hesitant to the Brutes from the beginning. Why allow them to join if they knew they could be a problem from the beginning? Pretty sure the Covenant committed genocide against other species before, or just ignored them.
Looking at the Halopedia it states in the Twenty-Ninth Age of Doubt:
"It is known the Kig-Yar ship Pitiless has brought forth an Unclean Being's corpse. Hear now, all Kig-Yar vessels are to be searched. Let faithful Sangheili lead teams of Unggoy to all Kig-Yar ships and seek further evidence of the Unclean. It is done." — High Prophet of Restraint
And:
"Hear now that 500 teams are to be formed to study the language of the Unclean. Each team to consist of the most clever and most educated Unggoy and Sangheili. These teams to speak only the Unclean language among themselves. The Unclean language to be taught to all military strike teams, that the foe shall be vulnerable." — High Prophet of Tolerance
So who are the Unclean? Cause it seems this is before the events of Halo