Pretty much what I have so far gathered from the Flemeth/Morrigan story is thus
A) Morrigan is a true daughter of Flemeth

The story of Flemeth is that she continues living through her vessels, aka daughters, by possessing them as she gets old. Hence, the daughters of Flemeth legends, how the Chasind can recognize Morrigan as a witch of the wilds, and how both Morrigan and Flemeth state that Flemeth was once young and beautiful as well as had a likeness to Morrigan.
C) Being that Morrigan is a vessel which Flemeth plans to use, that would make Morrigan viewed as something of her greatest worth. Which she stated when she "gave" Morrigan to the Wardens.
D) More experience grants Morrigan stronger powers. Which, in turn, would become a stronger host for Flemeth, hence the payment "FOR" saving their lives was taking Morrigan along.
E) Not to mention, Flemeth also has planned that Morrigan would love one of the Wardens and would bear offspring from it. One of tainted power which would become the next vessel in line once Flemeth occupies Morrigan's body. Hence, the reason why she was willing to give you the grimore freely. So Morrigan would come across the Dark Ritual and use it.Thus providing a stronger and more powerful vessel down the line.
F) Flemeth doesn't fully die after you defeat her if you chose that route. The shade/spirit combo that is Flemeth, lies in waiting for Morrigan to return to the wilds as she has always done when she gets bored of the civilized world, or need the safety of the wilds. Being that she is very used to it and understands how to survive in it, which again was something Flemeth made sure to teach Morrigan as the foremost important things in life. Since she is making sure her own survival is guaranteed and that her legend remains intact.
Now to me this is all conjecture yet, since the farthest into the storyline that I have done is three treaties; dwarves, magi, and dalish.
As to the facts I seen posted here already, since I haven't gone through the entire story yet. I believe the two souls canceling each other out is a misconception that is shown in the game. As in this is what they "believe to be true" and not necessarily what is true. Like how the world was believed to be flat at one point of our own history.
The reason for that is four things. Flemeth, Wynne, abominations, and the possessed templars you battle in the circle tower. Such beings are either a soul overpowering another, or conjoining with another in a balanced agreement or pact if you will. The later being the Flemeth and Wynne stories. At least I think Wynne is conjoined, though I have barely even had her in my party let alone really chatted with her. Yet, since the Warden's will is strong enough to survive the initial tainting, they have the strength of will needed to fend off the Archdemon's soul so that it can't possess them but not strong enough to survive the attempt.
As Flemeth did state, the evil behind this blight is more powerful than they think. If Flemeth could grasp its power herself, do you really think she wouldn't? I really wouldn't be surprised if we see Flemeth again in DA2 and who knows maybe then we will have to battle her again, or for the first time as the case may be. Only that time, she could be the arch-villain.
That would be an interesting story to play out actually, at least IMO anyway.