It would also seem to require a superficial understanding of a number of events.
Cyclops was right to keep Hope out of the Avengers’ hands. Had he given her up to them, the world would have burned. The Phoenix would have come to Earth, and laid waste to everything. The war between the Avengers and X-Men was a necessary action. This is a world where prophecy, fate, destiny, and faith truly have value. In the big universal picture it had to occur in order for her to gain the perquisite experience to fulfill the purpose she was born for. How do you not know this?
I will backup a somewhat, and try to lock onto it for you, so that illumination may occur.
Cyclops never had a plan. He absolutely no idea how to bring mutants back to the earth, and never claimed to posses this knowledge.
When Hope was born, you might say Scott had something of a religious awakening. He knew in his heart that she would bring mutants back to the Earth. He was clueless about how it would be done, but he knew she would do it. This was a conviction he had to the core of his being. He believed it so much, he entrusted her safety to his only begotten son.
Everything Cyclops would do from that point on was simply a holding action. Keep as many people alive until whatever miracle she would pull off, happened. This was truly akin to religious fervor. That was the faith he had in whatever she would do.
It was not until later that the Phoenix would come into play, and it scared the fuck out of him. You may remember Avengers: X-Sanction, the comic billed by Marvel as the prologue to AvX.
He had his talk with Cable at the end, where he expressed his misgivings about the Phoenix’s involvement. After reaffirming his faith in Hope, he accepted the Phoenix would be part of this.
Scott would also learn from Cable that the Avengers would come for Hope, soon. He saw the world that would result, if they were successful in taking her. He was literally given a glimpse of the future that would come if he gave her up. Beyond anything else, he had to keep that from happening.
Now let’s address some of that nonsense you spouted out about the Avengers’ plan.
They intended to “intercept or contain” the Phoenix before it got to Earth. Destroy it if they could. To say that backfired is a grand understatement.
Their backup plan was to keep Hope in “protective custody”, away from the Phoenix at all cost if that failed.
Wolverine intended on killing her.
You mentioned the K’un Lun, and I am glad you brought them up, but they were not part of any plan the Avengers had come up with. It was not even an option for them until after they were getting their asses handed to them as a result of Stark royally fucking up.
This is where that prophecy stuff I mentioned earlier comes in to play. Those Kung fu folks had their own legends about the Phoenix, and their role to play in the grand design, that were independent of anything the Avengers, or the X-Men had any inkling of. This is a sign of the greater will of the universe at work! Seemingly disconnected flows were now joining up to complete cycles that had been at work for centuries. It can be pretty heady when you think of its magnitude.
It was from this point Hope was able to get training she would need from them. Spider-Man taught her lessons in responsibility. The whole tragedy that was AvX was part of the universe preparing her to harness the Phoenix, and fulfill her destiny. The notion that she defeated the Phoenix is plain silliness to me. She completed its cycle.
But before that happened, Tony Stark needed to have a moment akin to what Scott had, when Hope was born. After Hope had completed her learning experiences, he would reach a point where he was able to accept the Phoenix needed to complete what it had started, and took a leap of faith. Harmony of the universe, and all that jazz.
He would even admit later that he knew what the consequences of those actions would be.
Fate does not move at the behest or mortal men. The mosaic of the universe is not visible, and requires a multitude of pieces working in concert. After the universe (you can might even be able name it as Eternity) had completed all its action, we were back to where it started. Hope saves the day.
The faith Scott placed in her from the day she was born, would end up being validated. Not having a plan worked out to his benefit, and played to his strengths. Cyclops thinks on the fly, and adapts to the situations on the ground, as they occur. He knew she was the key, and he had to keep her alive, so that she would take them across the finish line. He did so.
Your point about them not trying to reignite the mutant gene does not hold much water. They were not the correct hosts for the Phoenix, and had it forced onto them. They were twisted by its very presence in them. Hope needed to release the Phoenix in order to restore the worlds mutants. Even with all she had gone through, she had a wavering moment before she was able to complete the destiny she was born for.
Captain America coming to Utopia was a fulcrum moment in the history of the Marvel Universe. When it came, Cyclops made the correct decision that would set in motion a chain of events that ended with the Phoenix restoring mutants, and continuing a long tradition of not destroying the Earth.
I have been explaining this shit for 2 years, now.