Getting back to the start...
It's said Vivienne is going to be very much about the Circles and their benefit to Mages, looking down on Non-Circle mages like Solas and generally having been dragged kicking and screaming into "freedom" by the Templar vs. Mages war. I was contemplating the implications of freedom and how people would support the system and was thinking of something which the game may or may not deal with.
Specifically, that without the Circles, Mages as an identity wouldn't exist.
Mages are, with rare exceptions, a group without national ties. The Chantry dumps them all in the Circles together so Mages are loyal to each other, elf or human, rather than their respective home nations. The Dalish illustrate the problem of Mage freedom as their Keepers have no interest in the affairs of Mages because they don't self-identify as Circle Mages. See Morrigan for how much she despises them all.
But yes, if the Circles dissolve won't this kind of break any power-block mages have? Standing together, they can protect their rights but if freed, they will lose all connection to one another.
The point you're dancing around here is the idea of a Mage identity, rather than mage power. The two, while related, are not synonymous.
Mage identity is, at this point, a reality. It does exist in its current form thanks to the Circle, but we've also seen that it historically exists without it. In every Thedasian culture we've seen, mages have occupied a specific and exclusive social strata and identity regardless of the presence of a Circle system or not. Whether the Tevinter oligarchy, the Sarebaas, the Seers, Shamans, and Keepers, mages have routinely been categorized and lumped together by themselves and by outsiders. Mage identity routinely exists of its own nature, and will almost certainly continue to do so for the Circle of Magi as well. It may change slightly, but major changes will only occur over long periods of time and political divisions.
Mage power, however, is far more dependent on political organization. And this is one that may fracture after a victory... if political geography forces it. The Circles have become a unfiied polity, and will continue to be one for some time in any Mage Independence outcome that does not see the mages trade one supervisory institution (the Templars) for another (such as the nations). If Mages are independent, it will almost certainly be in the context of a Circle and alliance of Circles, and the less integrated they are with multiple alternative institutions the less likely they are to separate as a polity. Unless the Circles are split up amongst the nations, there is no obvious reason why the Circle identity would devolve in mage independence.
A much more plausible way to destroy the Mage Identity comes not with mage independence, but mage defeat. If the Templars regain the position of arbiter and enforcer, they can play internal divisions amongst the mages to break the solidarity. By unevenly applying benefits and punishments, encouraging mutual suspicion and distrust, and separating the various mage interests and priorities from eachother, the Circle as a polity could fracture into its component parts- which is to say, the Fraternities. Divide the fraternities into groups with mutually exclusive goals and interests, and you could easily go from residents of the Circle identifying themselves as 'I am a Circle Mage' to 'I am a -Insert Fraternity- Mage.' When a mage would first identify as Lucrosian, and only then as a Circle Mage, the Mage polity would be broken.