My headcanon about it, specifically in Halo 4, was more or less "Unless it's translation, why would they be speaking in English to each other", which is probably why I'm not as annoyed as most other people regarding the Sanheili language with subtitles.
Quote
Onto ONI, "These guys were the military sword for The Covenant. We need to make sure they can't threaten us ever again", 'were' being the key word, the elites were the UNSC's main allies at the wars close with the brutes having taking the elites main place in the Covenant, I still can't understand why they want to attack their allies instead of the actual brutes that should still be a big player in universe, but then they have just completely disappeared for some reason.
They really weren't allies yet. Since the third book in the Kilo-five trilogy hasn't been released yet, and it hasn't been mentioned in the games yet, it's possible some of those plans ONI was going through with were cancelled.
In fact, I'm almost certain they were. Some dialogue in Spartan Ops, specifically that one odd Sangheili Terrorist who tried to detonate a Havoc Nuke in a city. Perhaps an alliance with Sangheilios went through, and some Sangheili now live on Earth, and vice versa for Humans on Sangheilios? At least, I would assume a Sangheili getting into a city on Earth would be nearly impossible otherwise.
As for the Brutes, they weren't actually on level to do any damage to Humans, at least not for a while. They were more equivalent to what Humans are modern day, right now, before the Covenant adopted them into their ranks. Once the normal Covenant fell apart, they likely had more trouble than even the Elites at recovering.
Until its confirmed in canon later, though, it's currently all speculation. Still a good couple of years till the next game, so we'll just have to wait and see.