That already happens, mages are used in wars the chantry deems justified. The divine openly approved of Orlais' invasion of Ferelden, it was so bad the Ferelden king was about to burn all chantries in Ferelden. Not to mention when there is autonomy in circles mages are the ruling themselves as they always should have. The Templars are only tasked with protecting them from mundanes and vie versa. Claiming chantry is neutral discredits your argument as the Chantry is fully and completely on Orlais' side.
*snip*
The grand contribution the Chantry of Orlais; and there is a difference between the Chantry of Orlais and that of Ferelden; provided to the Emperor was three mages and moral support.
Three mages; that was how non-neutral the Orlesian Chantry was which is only expected; the Chantry of Ferelden eventually condemned the occupation when it was not certain death to do so.
And when the Blight ocurred, seven mages were. Just seven.
Three mages in a war between human nations and seven against Darkspawn.
Now, do you think nobles would have the same restraint and not send hundreds of mages against their enemies? Hence why the Chantry is neutral.
You keep saying "autonomy" but do not explain what autonomy means and how it would differ from the current state of affairs. For instance, autonomy, in my mind, would implicate the freedom to not live in the Circle, to be employed by nobles, to be able to live, never mind visit, in a city without having Templar supervision, to be able to own land or businesses.
If you think that I am nitpicking, then you need to properly detail your "plan" or, obviously, it can be filled with holes.
As it stands, I am already having problems with it:
"The only difference is mages are governing themselves and the Templars answer to the state."
Ok, so let's say a king wishes to have the mages fight in his army; he offers them wealth and noble titles, etc. The mages accept.
Then, this king starts using peasants to fuel blood magic. The mages do it. He goes as far as to select weak mages to become Abominations and be released into enemy lines; demonology too is allowed for the sake of victory.
Now, usually, the Templars deal with this except the Templars answer to the state and, therefore, the king forbids them from doing anything.
Or, what about this? A noble suffers a terrible monetary loss. The lucrosians lend him money. Through this noble, the lucrosians start influencing politics. Usually, the Templars deal with this. Except they are beholden to the state and the lucrosians pressure the noble to pressure the monarch to block Templar efforts.
Hence why the Chantry is important. Because it is an international, neutral organization capable of controlling magical incidents and keeping mages away from politics.