After Cage became an Alpha and entered the nervous system of the Omega, could it be the Omega that revives the Human-Alpha and not himself, to lure him in a trap by sending him visions ?
Carter said that Cage had the power, but I'm not sure of this. He never seemed to control it and I know it doesn't mean he didn't have it but maybe the Omega still had the power and wanted to make him believe he had it to kill Cage in a trap.
Besides, when the Squad J is in the plane to Paris, Griff said that Cage told them not to kill an Alpha because the Omega would replay the day and all would be lost. Wasn't Cage supposed to have stolen the power from the Omega ? meaning that it couldn't still have this power. If he never had and controlled it, why the Omega didn't just replay the day on its own, like it did each time the UDF won a battle ? I'm not sure it needs the death of an Alpha to reboot, because it would mean that humans have killed Alphas in almost every battle lost by Humanity and that the Omega would have replay all these days to win.
It seems very incoherent to me. Or I really don't understand a single thing in this.
Anyway, I think Cage never had the power. After many deaths and a good knowledge of his enemies given by the Omega (which was replaying the day all over), Cage was now trained and capable to survive long enough. It let him reach the point it wanted (for Cage, the dam, for Rita, Verdun) and made him believe it was there to kill him slowly.
For Rita, it was slightly different as the Omega wanted the Humans to win the battle but probably didn't expect her to kill an Alpha and enter its nervous system. Then it pulled her to a place around Verdun with false visions where Alphas could kill her. The Omega sort of trained her to win the Battle of Verdun and then to come in the trap but she finally lost her ability during the fight and was no more a threat to it. Then its plan continue with the Operation Downfall.
In the end, the Omega is dead, and can't revive by time travelling since its blood melt with Cage's like did the blood of the first Alpha... which never reappeared on the beach. How to explain the final time loop ? it could possibly just be the deep and unconscious willing of Cage with his new power. Anyway, the Mimics and the Alphas are already dead before the Operation Downfall since the Omega is no more. Rita is alive and Cage will tell her in details how the Squad J and her helped him to kill the Omega. The happy ending is not so bad.