If there are no Templars, the nations of Thedas will set up their own magic police force. So, instead of one that is built on ideals and devotion to a higher calling, you will have some built like that and others that are built solely to be the strong arm of local lords over mage subjects.
If the Circle is just going to become a bunch of boarding schools (Xavier's School for the Gifted, Hogwarts, etc.), then they are going to be under the watch of the nations they are a part of. Why would the nations grant them political immunity? The only reason nobles weren't Tranquilizing their mage subjects, drafting them into the military for raiding local noble rivals, or whatever nobles do to their subjects is because the Chantry said the nobles have no hold on the mages. The nobles and royals obeyed such things because they were either devout or their devout populations would revolt against them. The mages would have no such political immunity anymore and would fall under the laws of the nation they are stationed in and they won't be able to force nations to supply them with mages to train.
While I do like the Circle system and the purpose the Templar Order, I don't really have a big issue against mages just becoming citizens in their respective nations, with nations dictating the rights of their mages just like their own citizens, and having their own magic police force.
I don't like the idea of the mages becoming an independent, landless nation. Unlike the Wardens and Inquisition, they are not some giant mercenary force, they are more like a nation at this time. They'd just be like the Dalish, with nations not caring unless they get something out of it. The nations might as well ignore the College and start their own schools unless the College accepts the local laws and decrees.
Downside would be more mages in wars or skirmishes in the south. Upside is more research into anti-magic technology or whatever to reduce the impact of mages in enemy forces. Perhaps enough would be produced that commoners or at least lower nobility can afford such things. Anti-magic enchantments, wards, or devices could end up making mages just interesting fellow citizens who can't do anything too major with every building in a city casting its own magic nullifying aura.