If the Templars have no say in it, you might as well break away entirely. See where that takes you. For better or worse.
Trying to maintain a Circle system specifically though is acknowledging the Chantry. And acknowledging the Chantry means Templars or some policing measure as well.
There's an important distinction: the templars cannot operate independently of the Chantry. If, in this hypothetical, the Chantry is governing the Circle, then the templars are there as the equivalent of national law enforcement, like the FBI. Obviously, they have an important role, but actually having them run the daily life of civilians seems, to me, to be blatantly unjust; only the Chantry and the Enchanters should be able to pass laws (and if the Chantry is making the laws, it should have a representative portion of mages within it as well).