Hopefully these events/ideas haven't already been stated, since replying before reading all replies is sort of a general forums taboo(read 5 and got antsy...). Also, just to be clear, I really have not cared for how Traviss, and 343i if her books are the basis for how humanity will be in the coming games, has depicted past Halo events and established the UNCS(mankind) as it currently stands. That's another topic for another time(I.E. Halsey chronology being skewed to single her out as some sort of 'monster', Earth's Inner Colonies were bypassed considering Earth was found by accident, what happened to them? Brutes living alongside humans.... Jackals, ok that's sensible, not abominable gorillas)

As for the state of the Covenant, I'm really not all that surprised and don't see to much wrong with, if you look over the fact that the Arbiter somehow lost all the prestige he had with the surviving elites. To start off there is the destruction of High Charity, which was just about quite literally itself infected by the Flood, and eventually completely obliterated. On top of that there's the Great Schism having its main brawl fought between High Charity's now divided fleet with both sides being pretty much decimated, especially since the Flood took part in the fight. Lastly the savior Master Chief himself along with Blue team taking out the Unyielding Hierophant and the massive fleet standing by around it prior to the formerly stated events. I'd say that has to account for a large majority of any authority and military might the Covenant held.

Regarding the 'Covenant Empire', much territory may have been conquered by the Covenant and therefore considered within their domain, but I always regarded the Covenant as existing more in the manner of flotillas. Each race still existing on their planet of origin, Sangheili I can see having a few colony worlds, other than that I viewed the Covenant as populating mainly ships, space stations in the manner of relay points and supply depots, and any planet-side infrastructure being for industry(mines, factories etc) and worker housing. This is just how I see it though, if canon exists that describes the Covenant Empire or just disproves what I said, then back to square one I guess.