I don't think the point of the religious leaders was that bad. Yes the game doesn't explicitely outright discuss why these crazy dudes are in power, but you're probably not thinking in terms of the game if you can't relate. From the Covenant perspective, they're not crazy murderous monsters. This is the exact same thing as the perspective of a middle-eastern refugee whose house was destroyed by the superpowers (US et all) whilst they try to reshape the region. Those people are real, and you better believe they don't think too highly of anybody in a Capitalism state (ie, sympathetic to terrorists).
From anyone's perspective who believes in them, those terrorists aren't evil murderous killers. They're necessarially-murderous freedom fighters doing what needs to be done for their homeland. The same thing happened in WWII, when the Nazis killed millions of innocents; they didn't think it was evil either. Covenant wouldn't think they were horrid monsters doing horrible things, they're just following their mislead leaders (misled by our perspective).
I'm not sure where anybody would find fault in that. It has happened half dozen times in the past couple hundred years.
Realistically (in terms of the game anyway) the Covenant were clearly onto something in that their "great rings" would propel them to.....well, somethingorother. But it was presumably the afterlife that they were striving to reach.
It's a given that they would have to die to get there. But think about it for a second: given that the passage to Christian heaven usually requires death, perhaps the Covenant were right all along. That might have been the point of the game creators, who knows.
Of course the counterpoint to that is, to get there[afterlife] you have to kill everybody in the galaxy, so the point of the game's plot is to avoid that. Hey I'm interested to know if they were right, but I wouldn't want to kill everybody around me to find out...I assume you would feel the same. Know what I mean?
I just mean to point out it's difficult to sit there in our nice quaint armchairs and say "I don't believe that is realistic cause I wouldn't do it". You have to actually think about the story and its ramifications, and relate to everybody involved, even if they have two pairs of knees

Alleged generic action shooters rarely have you put the thought into it, whic is one of the points in halo...you can still blow stuff up and not think one second about it. It allows the game to please both the fratboys with rocket launchers, and the science fiction fans and historians.