The Witch hunt Dlc is romance and/or DR specific but for all others world state doesn't make much sense.
Oghren doesn't know anything about Morrigan and is even removable as companion(refuse to recruit) while Alistair can be killed or exiled so that he don't even meet the Orlesian warden,there you have it a character who is not fitting to play WH and it is just one of many.
Even those wardens of Origins who couldn't care less of her wouldn't have wasted their time to chase her after the soul destruction of the Archdemon in the non-DR world-state.
Oghren spendt the better part of a year traveling with her and several companions who were very vocal about why they didn't like her. There's no way he wouldn't have picked up on her history. In any case, the events of the Blight would have been scrutinized after the fact by the order at large and Morrigan's presence would have elicited questions about the strange apostate who voluntarily traveled with the Warden, is rumored to be one of Flemeth's daughters and left right before the final battle under mysterious circumstances.
The Orlesian Warden Commander could have orders from Weisshaupt to find and interrogate her, as could a Warden who didn't perform the ritual, and even one who did. One might go looking for her after hearing she'd been spotted just to make sure she wasn't getting up to more trouble, like trying to locate another Old God to get an extra shot at its soul. That danger would seem especially pressing after having learned of the Architect's involvement with prematurely starting the Fifth Blight.
There are plenty of Wardens who wouldn't go to investigate a failed expedition to look for a long-lost thaig either. Morrigan and the Dark Ritual was a major loose end that really stuck out until Inquisition. There wasn't nearly as much call for a Leliana-prequel or a playable what-if scenario like the Darkspawn Chronicles. And if going in search of Morrigan really doesn't suit your particular warden, nothing forces you to play that particular DLC.