Well let's see. I just saved Orlais and created true peace between them and Fereladan. They are my most powerful ally and I am not about to let another Blight (you never know) wipe them out because of a choice I made based on what happened in that moment (to Wardens who stood down and refused to join in the blood magic) and not throughout history (Sophia being an exception). Not only would I get blamed and our treaty strained, but I would be endangering future generations. Until the Blight is truly ended or cured, Wardens must be rebuilt stronger and better.
What happens to your treaty when the Orlesians find out that the Wardens were involved with the death of the Divine?
Because the Wardens were banished from Ferelden 200 years ago (for taking the wrong side in a revolt against a tyrant), yet remained distrusted all the way to the present day. This left them most vulnerable to a Blight when another Archdemon woke up since the only people able sense and predict them were too few and too distrusted to effectively quell them before they got out of hand. I personally don't think it's any coincidence that when an intelligent, thinking, cunning Archdemon awoke, it went for the country with the least amount of Grey Warden presence, welcome, or activity. One can't help but think that if Ferelden would have been a lot better off if they had forgiven their centuries' old grudge much sooner.
For DAI I saw that pattern rearing its ugly head again, and decided to nip it in the bud. (Banishing them from Orlais seems beneficial in the short term, but in the long term you can't predict what the darkspawn will do, what new tricks they'll pull up their sleeves, or where or when the next Blight will strike. So better not fire the only firemen of your world assuming the flame will never come back to your door.)
I'm thinking that despite all that, Ferelden came out of the 5th Blight smelling like a rose. There are places on Thedas that have yet recovered from a Blight. There was even debate that what they had was even a Blight at all, considering how fast it was dealt with.
Why wouldn't you exile the Grey Wardens? Easy answer.
King Alistair, Bethany Hawke, "Blackwall", Carver Hawke, Daveth, Duncan, Garahel, Hafter, Kristoff, Larius, Loghain, Ser Mhairi, Nathaniel Howe, Oghren, Riordan, Sigrun, Stroud, Velanna and someone that we are all familiar with: The Warden / Warden-Commander.
My point being that even with some of these characters personal back stories, they all proved to be honorable and worthy members of the organization. There are also others tied into a few of these names to which the same inclination is evident. We have seen, read and/or interacted with far more decent Wardens than those few leaders who took the entire order down the path that led to their role in Inquistion (and all done under the pernicious influence of Corypheus); plus Warden-Commander Clarel redeemed herself, at least in my eyes, once she realized that she had willingly allowed herself to be duped (and again, despite the harshness of her actions, for the best of reasons).
Try riding out the next Blight with the Warden's gone the way of the dodo?
Since they won't be gone in the way of the dodo, but simply exiled, I don't see what you're getting at? It would seem that you have confused extinct with exile. They are not the same thing. That was a fairly common thread earlier on too, people acted like exiling them equated to putting them to the sword. This is not the case, and the duration of the exile is left, I suspect, deliberately unknown. For me, I can see lifting that exile, after the immediate threat is dealt with. Cory is able to influence them, and that's not something that can be readily dismissed because "Blight". It does make them a potential threat. We, of course, have the knowledge that it doesn't matter either way, and some of my Inquisitors have chosen to overlook that detail in favor of keeping them around.
Regarding your list, that an impressive list of people that could be dead, some before they ever became Wardens. Bethany or Carver will die on the way to Kirkwall, after all, and there's no certainty that the survivor will become a Warden at all. Bethany can end up dead or in the Circle, depending on choices made going into the Deep Roads, and the same applies to Carver, only in the Templars. In my world states, Alistair is dead. In other's world states, Loghain is certainly dead, if Alistair is King. Alistair can also be off in the Marches, being a drunk too. So really, there's not a lot of prime real estate in your list. There's a lot of potential, but not a lot of prime real estate.