Also, while thinking about the original question, the Covenant failed in ever stopping the Flood or cleaning up their mess. For all we know, the destruction of the Halo at the Ark didn't actually take out the Gravemind or the Flood there, potentially still leaving them as a threat with a potential ability to get off of there and do something later.

Within Halo 4's own campaign, at least for now, Master Chief and Cortana dealt with the Didact. Like the vampire he is, Master Chief thrust a stake (grenade) into his chest and took him out. Sure, I don't believe he's dead for a second, but at least in that campaign alone he's been dealt with. To parallel H1, Master Chief also dealt with the Flood right there in that campaign, too, effectively cleaning up the Covenant's mess. Unfortunately, in Halo 2 the Covenant screwed up again at Delta Halo and let more Flood out. I think Master Chief's got this, and I don't think comparing his fail to the Covenant's works at all.