I'm glad I'm not the only one who was confused by this. The only real reason I can think of as to why the hierarchs would want the elites out of the picture BEFORE Regret was killed would honestly be the destruction of alpha halo. But even then that's sort of a sretch because they go from barely trusting the brutes with guns to suddenly thinking that they're the cream of the crop of the covenant. And they really do just frickin crumble! I was thinking about halo 3 the other day and realized how utterly inconclusive it really was. Truth dies and just like the entire covenant is gone, even though there are other Prophets who could have taken over the hierarchs position. They really did go from being the biggest threat in the universe to clowns from one bad decision. And a decision that really didn't even make sense.
The story with the prophets is they were all conviently on high charity thus between high charity falling, and the victorious elites being on the warpath, that they quickly crumbled. At least Jul's covenant stayed around as a force, despite some people's dismay, because to be honest, you don't kill a multi-thousand year old empire/religion just by killing off its leader. Many leaders/popes have been killed and their little countries on earth survive them.
I'm guessing the elite rebellion was thought up to try and make it make a bit more sense from a writing point of view, but its just weird how Truth decided to enact this plan so close to just winning anyway. It wasn't even Alpha Halo's destruction that was the cause, because the Unyielding Hierophant was already staffed entirely with brutes and ready to invade earth, presumably because Truth didn't want elites involved.
And why? The only reference I can think of is some little nugget about elites questioning why humans weren't offered a spot in the covenant. This is of course, not in game (I don't know how bungie gets away scott free for not including essential things in game) and I believe only in the bonus material that came with the halo 2 special edition or something.
Even if Truth had been planning for a while to dispose of the elites for questioning him, its to be the most moronic thing to do so utterly close to victory. They had the Index, all they had to do is bring it to the control room and they win. I dont think this is a hindsight 20/20 thing. The brute uprising is triggered AFTER victory becomes super easy, barely an inconvenience. Instead of the schism, they could just park all the covenant around halo's control room, and activate halo with little problem.
In this case, the Gravemind just has John to move around to save the galaxy, which I'm presuming he'd send to the control room while the flood attacked high charity much like it did. I don't think a united covenant would have saved high charity either way, but the united covenant all parked around the control room would have likely slowed John down too much to stop them, even if we fanservice chief into being able to shoot his way through the entire defence forces.