The OGB isn't Tainted. They were at conception, but not any longer.
Aye, the goal of the Dark Ritual was to get the soul of the Old God into a new vessel that was free of the Taint.
Although I've often wondered whether the OGB was even tainted at all, even at conception? The Taint present within Grey Wardens seems to be located within their blood only and not within any bodily fluids, since we know that they are able to sleep with people and not risk spreading the Taint to others?
The way I figure it, the Dark Ritual may have been designed to be similar to the process in which the Archdemon soul-surfs through the Taint, only using blood and a familial connection instead. This was presumably modified from the same ritual that Flemeth uses to possess her daughters, which seems even more likely since Morrigan tells us that the Dark Ritual was apparently a creation of Flemeth's?
My theory is that while the Archdemon does use the Taint in the Warden's blood to try to jump into them, the Dark Ritual simply makes it so that once that occurs, the Warden's blood is then replaced as the base element instead, which allows the Archdemon to then be shunted into the OGB via their patrilineal blood connection?
Further credence to this is that we see something similar with Yavana's plan to use Alistair's blood to reawaken slumbering dragons in "The Silent Grove", where much like the OGB never being tainted despite their father being a Warden, Alistair is not a Reaver, yet nonetheless possesses the same blood as Calenhad who was (allegedly) one, allowing for the ritual to work?