Exhibit A - Captain America has a plan and its been described several times. Are you reading this event? They are going to get Hope off-planet to meet the Phoenix somewhere where there is no collateral damage, assuming that the Phoenix is coming for Hope (note: if you say that is a bad assumption, it is the same exact assumption that Cyke is making by training Hope and no one else...so...yeah)
Exhibit B - I am not defending Wolverine. Nor is Cap. This is to Cap's credit, remember? Oh...right, nothing can be to Cap's credit.
Exhibit C - Cyke's plan is not the "only one with a slight chance to work"...that doesn't even make sense. If the Phoenix meets up with Hope in space its literally exactly the same thing as what Cyke was planning (training Hope to host) except it removes the possibility of collateral damage. If there IS collateral damage, Cyke's plan is the only one that results in the absolute obliteration of humanity and the Earth...not Caps.
Exhibit D - Cyke is unaware of the flashbacks in New Avengers so using that to bolster the intellect of his plan is a stance that is disingenuous at best, stupid at worst. Also that story is unfolding...maybe she flips out and has to be killed by Da Vinci...that story could go anywhere. Besides, with Bendis' ability to follow his own continuity, maybe she DOES destroy Earth because BMB forgets that the characters he's writing about in the present are on Earth. Could happen.
So yeah...your logic? Can't see it. Sorry.