I think you're right. She's crazy powerful, obviously, but I don't know about her manipulating everything to such an extent. So far she's been prepared to save a person or two and then just stand back and let the world burn itself to the ground if that's the mood its in. The Warden she definitely had a vested interest in saving for the sake of the stopping the blight, (plus the old god soul thing though that hasn't really gone anywhere,) but I find her reaction to Hawke the most telling.
I don't know... I said so much "maybe" because I am not decided.
I wouldn't be surprised if she was a player, but I wouldn't be surprised if she was just an observer either. Really, what I'm writing here is not "my opinion". I don't actually have one. I'm just coming up with possibilities, nothing more.
In any case we do know one thing, which is that Mythal is not all passive. She does act, occasionally. She saves the Warden because she needs her. For some reason she considers the Blight important. Whatever reason is trivial; maybe saving the OGS from the archdemon is what she needs the Warden for, knowing Alistair alone can't make it and the others are nowhere to be found. I can see different ways of saving the soul; if Morrigan didn't bear the child, somebody else might have, or Mythal had another vessel at hand thanks to yet another ritual etc. We don't know whose soul it even was.
She saves Hawke for similar reasons. I don't believe she saved her for the errand. When meeting on Sundermount she makes it pretty clear that this wisp was a minor artifact and of little importance, she had others around. So she needed Hawke, maybe because of Anders or whatever. BW doesn't refrain from time travel, so maybe seeing the future (and only acting to make sure it will really happen) is also in their books.
The only thing I do have an opinion on is that Mythal could interfere. If she wanted to. That she doesn't could have many reasons.
She more or less just looked at them and thought 'You are going to mess sh*t up. Want a lift?'
That's not the attitude of a chess master artfully manipulating the players. That's a tired old woman who doesn't really care any more but she'll stick around for a good show.
Here I have another opinion, but that's really just my individual feeling.
First, because I never thought Hawke had messed anything up. Hawke only accepted jobs and did what she was asked to do, nothing else. How things turned out was never in her hands. She was not responsible, she was only helpless.
If Hawke hadn't been there, Bartrand and Varric would have ventured to the Deep Roads with somebody else, still finding the idol. Also Orsino and Meredith would have started the same war. Anders (controlled by Justice) could well have still blown up the Chantry. Maybe it could have all turned out even worse without Hawke?
Second, I am not convinced that the events in Kirkwall can even be considered a mess. After all they forced a change, forced to break with the old system (circles etc.) that hadn't been working for a while. Red lyricum was released upon the world, the political situation was affected, and maybe whatever happened there (I once read a theory about Kirkwall being a place where magical powers intersected, and events there influenced other places of Thedas) might have aroused whatever forgotten powers.
So while I acknowledge you could be right, I don't necessarily think that Mythal didn't interfere because she was tired, but because she wanted the events to unfold. As Solas says "action is not inherently superior to inaction". When I played DA2, I thought it was Mythal's plan for Hawke to get involved in all of this. Sort of an enabler. You see the person you (1) saw when looking into the future or (2) you think capable of being "the one". Because why did she save her for an unnecessary errand?
But, again, I have no fleshed out opinion. It's all only based on the feelings I got when playing the games. I'm not one to read codex entries and make connections.
I could be completely off; and I know how everything is possible. Hence, I said, I barely ever state an opinion but ideas on possibilities.