This definitely depends on how you roleplay your Inquisitor. My canon one went through a long emotional journey throughout the Inquisition years, and by the end of it she was just very tired of it all. She was exhausted, physhically and emotionally, and just wanted out. In the end I didn't disband the Inquisition because the Council demanded so, or because I wanted to play secret cabal against Solas, but because I felt Ariana was genuinely
tired of being the savior of Thedas. She
wanted the quaint, cheesy happy ending, she wanted to go live in the countryside and pet mabaris with her husband and do good work on real-life matters that affect them directly; she didn't want to fight archdemons and ancient magisters and vengeful elvhen gods anymore.
She never felt responsible for Solas either, so much as just used by him, which didn't help the feeling that she needed out of this mess before it destroyed her. Is it a dangerous kind of apathy to want to just let go of the threat of Solas and let someone else save the world this time? Sure is. But the two lines that most marked Ariana in my playthrough were Cullen saying "I've found certainty in my life now" and Solas saying "live well - while time remains." It was a warning, and after waking up with half an arm missing and realizing Solas could've simply just killed her right there and it would all have been in vain, Ari realized she wanted to heed it. The things that really mattered to her -her love and her friends- were right there, that was the certainty she found in her life, and she would rather just live while she still could.
Of course, then BioWare throws that post-credits scene with the little cabal and foils all my headcanons again.
But that's why I have such a hard time seeing my Inquisitor heading any significant force against Solas moving forward, leave alone actively hunting and personally fighting him - because she's done with all this. If she shows up again in DA4 in an advising capacity, or even just a side NPC offering intel on her experiences with Solas etc to the real new hero of the week who's going to take him down, like Hawke did with Corypheus, I'll be more than satisfied.
I mean, I do recognize that many (most?) people will feel like their Inquisitors are personally responsible for Solas and should be the one to take him down. It's a valid feeling, one I thought I would have by the end of this DLC too, but it didn't quite work out like that, for some reason. I'm just explaining why mine doesn't want anything to do with that, which is why I have such a hard time picturing her as a returning protagonist. Unless Solas went full Disney villain and came down to the Fereldan bannorn to brutally murder Cullen in front of Ariana or something just to rile her up, she just doesn't have any fight left in her for him anymore.