It's like reverse Daenerys. Instead of shedding someone else's blood to birth the dragons, you shed dragon blood to rebirth the world free of Blight? Very, very creepy. I like it. There's probably something particular about the blood of the Old Gods too. The Wardens need a drop of Archdemon blood (in addition to normal darkspawn) to create the concoction for the Joining, otherwise it doesn't work.
Exactly. I've always thought it very interesting that you can only do the Joining with Archdemon blood in the mix - their particular brand of "insulation" against the taint without actually being free of the taint is an indicator of something I'm sure. The whole process of the Joining is reverse engineered to begin with, so logically you could do the same with the world in general, but it makes much more sense to me that to truly be free of the taint, it moves on the same axis of "natural corruption," i.e. a "clean slate" rebirth.
What I mean by that runs along these lines: the taint is a natural phenomenon, thus a rebirth of some sort is required as a counterpart to that as the only way to completely distill the taint and yet retain the key essence. Like matter and anti-matter; one cannot be destroyed without the other, yet one cannot exist without the other, so the only way to get out of that logical loop is to have two polar elements cancel each other out of existence.
Again basing this on alchemy, the first step to a true transmutation begins with destruction (the utter corruption and disintegration you could say, so the taint in this context), then a distillation of all the components (so we have Archdemon blood, magic, birth, regular darkspawn blood and Grey Warden blood, which again is a new formula), then the recombination of these elements (i.e. in Fiona's case we have a Grey Warden, tainted by both darkspawn and an Archdemon, who gives birth to a distilled part pure dragon-blooded child) and finally the rebirth itself (the distillation is completed in the child's construction).
I.e. this is basically the same process that Kieran's birth signifies, which we may recall involves powerful, ancient magic that Morrigan uses to "distill" the Old God from the tainted Archdemon. The question is how to expand that process to a larger scale. I think it significant that Fiona is the only Grey Warden mother we know of who actually is cured of the taint: that tells me that some element unique to her situation was the cause, and Theirin blood in her body is what makes most sense. Yes, Alistair is not immune, nor would any Theirin's be by themselves, but as I said, I think it's not the blood alone, it's the process of growing a child that is what does the trick.
It could even be that Alistair ends up fending off the taint after a while, or that his Calling is not quite as potent as that of a run-of-the-mill Grey Warden. Going on this, though, it could be that an infusion of blood from a Grey Warden mother giving birth to a Theirin child could give just the right combination of essences... hmm, if your Warden is Alistair's queen, would that mean your Warden could be cured of the taint as well, should she succeed in conceiving a child from Alistair...?