True. After Trespasser, I see that many underestimate the power national entities have in Thedas. It's true that there's still a long way before the setting sees something similar to the Westphalian state, but the Chantry and other international organizations like the Inquisition aren't all-powerful. Like when most of Kirkwall's problems started when the Chantry tried to do Orlais a favour in a matter outside religious, Circle or Templar matters. Or when Gaspard, before the civil war, suggested the use of the Orlesian army to crush both mages and templars. If Celene disagreed wasn't because she thought it unfeasible; on the contrary, she was afraid the bloody success would undermine her peace-loving public image.
Which those precedents, was it so difficult to imagine Orlais and Ferelden together trying to put the yoke on the Inquisition? It wasn't. The same could be said of the College, which shouldn't work with at least some sort of arrangement. Vivienne's ending if Leliana is Divine suggests that even her Circle gets its power from its "political connections".
What makes it worse is that the status-quo for the mages is unsustainable.
When the Chantry ran the circles as a mage monopoly, they had the heft and monopoly to keep the mages from being political footballs or national advatnages. Everyone accepted this, more or less, and the Chantry's allowance of mages was restricted enough (Blights and Exalted Marches predominantly) that mages weren't a strategic advantage.
But while the Circle could maintain it's monopoly, the College's can't. The inherent nature of mage freedom is that the mages will be free to make deals, and bargains, and be sought for such by ambitious patrons or nobles. If the College even tried to prohbit such contacts, it'd just be the Circle. The College guarantees local political influences, and the competition between College and Circle will mean the Circles will be competing for the same patrons and influence.
That competition is going to break the idea of neutrality on an international level, and probably break the Circle and College both as international, rather than national, institutions. As the mages tie into the political fields, they become political influence and national assets. But no matter who 'wins' between College and Circle, they'll both be aligned with the kingdom... and drawn along when the Kingdoms come into conflict for their own reasons. It's easy to see the College and Circle having proxy battles if there was, say, another Orlais and Neverran conflict... but it'd also be possible to see College vs College or Circle vs Circle if their respective patrons are in conflict.
That breakdown of mage solidarity- what makes 'the mages' a meaningful description of a political identity- is what's going to ruin a lot of the hopes for mage freedom or the College. The more valuable and advantageous mages are, the more Local Colleges will either dominate, or be dominated by, local political elites. The more they are, the more the interests of the mage collectives diminish, and you'll see a fracturing of the mage groups along geographic lines. And the more fractured they are... well, the more actors and opportunities you have for a mage elite in a country, the more likely you are to see de-facto mageocracies emerge in different kingdoms or areas. And the more reasons for Mundanes rulers to dominate and exploit the mages they have.
It'll take time- decades, even generations- but the idea of mage freedom as being free of the mundanes is a mirage. The apolitical freedom is on its death bed, and it's only a matter before mages carve out political spheres to dominate or they are dominated and exploited far worse than the Chantry ever worked them.