The only secret the wardens should share is that an Archdemon will respawn unless it is a warden that kills it and that it costs them their life in the process. That would help minimise situations like Loghain from happening again.
Now imagine the wardens go extinct with all their information becoming accessible to the nations of Thedas before the fifth blight. It has been 400 years since the last blight and many people think they are merely myths. Do you think any of these nations are going to keep a 100% mortality rate legion operational for that length of time without their sole objective appearing? I doubt it, they would of been scrapped.
This legion costs resources to keep active, fairly constant and willing recruits as even attempting to join it is a death sentence. Using it as a form of punishment for criminals will not work at all, penal legions only work when there is an incentive for those criminals to fight, a pardon after so many suicide missions and so on. What incentive is there for these criminals to even attempt undergoing the joining? It is a guaranteed death sentence and they know it. They may as well have a quick death as far as they are concerned, counting on honour from those that more than likely have none, not going to work.
Now if a nation thinks I'll just mass conscript from my people if a blight does arrive rather than spend the resources on a standing legion, you have the issue of revolts that come with mass conscription and are hoping that some of your conscripted people actually survive, what do you do if a blight arrives on your doorstep and everyone you forced to attempt to join dies in the process, you have no current back ups so you are shafted.
So they reach out to another nation, well now this other nation can play politics, yeah we'll come save you but it will cost you half your territory. It becomes a bargaining chip and a tool of petty bickering between nations rather than a force standing for all of Thedas. It also leaves it open for sabotage, I'm sure we could trust Tevinter to not try to poison all of Orlais supply of blood, arranging for mercenaries to eliminate any standing force of tainted troops and leaving them open to a blight with Tevinter coming down and resettling Orlais after it falls. With a single force without loyalties to any nation this eliminates the chance of this happening, after all they are there to protect everyone from Darkspawn.
As blights threaten all of Thedas and require more than a single nation to stop it, a force beheld to no single nation is the most ideal solution. Giving away every secret of the wardens is promoting self interest among a time when unification is required to get the job done and would most likely see the next blight wipe the surface of Thedas clean of life while each nation vied to end up in the best position post blight rather than focus on just stopping it.