Dragon's are resistant to the Tait and not immune. The Joining ritual is taking in magically enhanced taint and that's why Alistair ended up getting it.
I originally thought it was due to fetus-alistair absorbing his mother's taint that cured her, but that doesn't explain why she ended up becoming immune to the Taint altogether. She can no longer get it via the Joining
There are a few other problems with that as well. Then he would presumably have to have become infected himself, or else an unborn child is purged of the taint before birth (which seems like given how the OGB works).
If he became infected, then with "30 years tops" he would be dead by DAI. If he was cured, then pregnancy would be a cure for mother and child, and the Wardens would surely have figured that out over that over a thousand years, and women would routinely cure themselves of the joining through pregnancy.
It seems almost certain it was the Architect's meddling. And if there's one thing The Calling and Awakening have taught us, it's the Architect doesn't know what he's doing, especially when he thinks he knows what he's doing. All his plans end in unintentional disaster and cataclysm. So likely he would not know how to do that a second time.
What I wonder is, that if someone learns how to cure the blight - either a Warden like the HoF or the Architect again - what would happen if you applied it to a darkspawn itself...? Are they made of blight and unable to survive without it, or would they become some new kind of creature.