Why exactly should the Inquisitor be concerned if society, whether for the Vints or the Qunari, implode up north? The Inquisition's jurisdiction is down south, more fighting up north means less fighting down south.
Another point is, the Chargers are like the Inquisition's mvp commando team. They've won battle after battle and uncovered conspiracy after conspiracy for the Inquisition. In a chess analogy, it would be exchanging a queen piece for a hint on openings of the opponents pieces. That's great if the Inquisition can deliver a checkmate for the Venatori or vints but then you weaken your organization and are dependent on a foreign power for intelligence. It's like an opponent so consumed with checkmating one opponent that they leave themselves vulnerable to other opponents, whether that be the qunari or some other nefarious organization seeking to take down the Inquisition.
The longevity of the Inquisition will be put into question if it is dependent on unreliable alliances. The people who fight under your banner, who you can hold accountable, inspire, direct- they are the ones who win the Inquisition's wars and keep the organization stable;not foreign intelligence. If people die, then they die. The Inquisition should be accumulating power and influence to combat the threat, and the people will be avenged. A queen piece is better than pawns.