Okay, here's my TL;DR thought about the debate scene. They're positing Crazy!Wanda as a Phoenix-level threat here. Based on my readings of the actual Dark Phoenix storyline and similar setups, if it comes down to a last stand then whoever's the last hero making it will be doing this exact same calculus in their heads. Flipped around, team leaders do a similar battlefield calculus before asking a teammate to go to near-certain or certain death.
It's hella hard, it sucks, and the Avengers aren't wrong to want to exhaust every other possible option (in this case Dr. Strange) first - but Emma and Wolvie are just bringing it to the table ahead of time. Emma could be more tactful (is she a dog?) but given the impact Phoenix was shown to have on the entire X-team of time, I'm not surprised it's Wolvie who says he expects them to do the same for him.
Killing Daken simply for being "a rapist, a murderer, and an all-around scumbag" would be jumping the gun - the supes are sworn to leave those to courts to adjudicate on case-by-case bases. (See also, DC's Dr. Light and the Joker.) Should Daken rise to Phoenix-level threat, then lethal force would be appropriate to consider.
I'm not familiar with the Cuckoo storyline, so I can't speak to that one; I guess my question would be, how close to the wire had it come to the Cuckoos being a Dark Phoenix-level threat to mutantkind? If the PE struck before all options were exhausted, Emma might be justified in hard feelings after the fact - clones and timebombs the Cuckoos may have been, if I understand the description given here, but they were human and they were Emma's responsibility. [/tl;dr]