Why Bhaal's plan for Durge kind of sucks
To get into dangerously speculative territory, I think making Durge and their urges as murderous as they are was hubristic on Bhaal's part, and that Bhaal's quest might be ultimately doomed even if Durge does end the world and "succeed." Even in the "In Bhaal's name" ending, I don't think Bhaal wins for long, and this is my attempt to lay out enough BG3 and Forgotten Realms lore to explain this interpretation.
CW past this point for discussion of murder/mass murder, animal abuse, and suicidality.
Bhaal's Inconsistencies
That one famous Bhaal quote really hits on his hubris for me: "I can destroy your kingdom, Bane, by murdering your subjects, and I can starve your kingdom, Myrkul, by staying my hand." This line has always struck me as bullshitting on Bhaal's part. He's the god of murder, literally saying "I choose (to oversee) death" as he chooses his portfolio, and on some level, if he doesn't kill, he would also starve himself. He's canonically bloodthirsty enough that "staying [his] hand" seems like it'd often be difficult, at best. Importantly, Bhaal lost the game of knucklebones between the Dead Three, and he chose his domain last. It seems like it'd be really appealing to say a grandiose line to save face in that situation, and it rings totally hollow to me because of that.
There are also some inherent contradictions in Bhaal's goals and tenets as expressed in the Church/Cult of Bhaal, and this dichotomy is fairly prominent in-game through Durge and Orin's ideological feud. Orin's philosophy of quality over quantity matches Bhaal's domain over ritualistic killing (and also the Church of Bhaal's general dogma), while Durge's philosophy of quantity above all is seemingly also professed to them by Bhaal himself. Their "mindless butchery" matches descriptions of Bhaal as compulsively murderous, while Orin embodies his sadism and cruelty. Like Durge and Orin, it's hard for these two drives to peaceably coexist—if you kill everyone, you can no longer cause anyone pain. There isn't really a non-contradictory middle ground here, and Bhaal does not strike me as a dialectically savvy guy.
The Consequences of Durge's Success
Global genocide, when taken to its ultimate extreme, could end up being just as destructive to Bhaal as it'd be for everyone else. To stretch the eating/starving metaphor to its absolute breaking point, if Durge fulfills their father's wishes, literally everybody dies, and Bhaal is gorged on the blood of all of Toril, but he'll starve to death after that anyway because there would be no more people left to feed him.
It's fairly well established that a god's power, if not their existence, is connected to the amount of followers they have, and if Bhaal's goal for Durge is fulfilled, they also kill every single Bhaalist. This pattern seems to show up in like half of the gods' wiki pages, but I think the Earthmother's limitations outside the Moonshae Isles is good example of this effect, as well as Celestian's growing influence giving him the potential to become a greater deity.
It's possible Bhaal could do what a lot of gods do and attempt to butt into a new realm/pantheon before he withered away on Toril*, but I think fulfilling his goals in the way Durge is compelled to would significantly weaken him, at minimum. I don't personally view it this way, but I think you could even interpret Bhaal's creation of Durge as the beginning of a murder-suicide pact with the world that his child then carries out on his behalf (in which case the title of this post is wrong, but oh well).
Now, for an obligatory reminder before I move on because I know I've been phrasing ideas too emphatically: if this contradicts your interpretations of BG3 or Forgotten Realms cannon, that's awesome, and I'd genuinely love to hear about why. If there is source material that contradicts my ideas, I'd also genuinely love to know where I can learn more. In posting this, I am only adding an option to the buffet—you can enjoy it, ignore it, or spit it in the trash, but please be civil about whatever choice you make. Moving on.
Bhaal's Influence over the Urge
I interpret the urge as an extension of Bhaal's will in a general sense, but I don't think Bhaal is actively putting thoughts into Durge's head as they occur. The urge seems to function largely autonomously without Bhaal's active oversight, but it was created to be a manifestation of Bhaal's very general desires and his most violent, capricious, and impulsive aspects. It's like a brain tumor that guides Durge towards Bhaal's ultimate goal of global genocide, rather than a direct remote-control.
Bhaal doesn't seem to have any capacity to read or even influence Durge's thoughts other than through the urges, and even this influence seems to be limited. Sceleritas seemingly can't find Durge prior to killing Alfira, and his concern about their "separation" could indicate that he wasn't even sure if Durge survived. Given that, I feel pretty confident Bhaal wasn't directly causing their urges before then.
Bhaal/Sceleritas can seemingly increase the frequency and severity of the urges like they do as punishment for not killing Isobel, but they don't make Durge actually want to kill her directly. I don't know why they wouldn't do that unless they don't have that ability at all (except because it's an RPG and players would probably hate that, but I'm speaking in a purely in-universe sense). Because of Durge's potential failure to kill Isobel, I also don't think Bhaal can reliably direct the urges to kill any specific target, even though the Act 2 scene's favorite companion mechanic and Sceleritas' dialogue can make it seem like that's the case. To me, it seems just as likely that Durge's fixation on that companion also causes the urges to fixate on them as they worsen during the Act 2 scene.
Sceleritas acting as Durge's evil Jiminy Cricket does a lot to indicate Bhaal's lack of control. There's no (in-universe) reason for Sceleritas to devote so much time to steering Durge wrong if it wasn't at least somewhat necessary to ensure Durge's compliance. Jaheira actually hints at this in some of her dialogue with Durge, and says outright that Sceleritas is unusually persistent. If you ask her if the Bhaalspawn she knew were ever visited by a "grotesque butler," she says "Bhaal had his minions, certainly. But none that watched over their wards so diligently" (I don't have a link for this, but I did record it during my last run, so I am confident the quotes are accurate).
Also, If Durge kills Orin in their duel, the initial dialogue with Bhaal plays out the same even if you've been spitting in Bhaal's face as much as possible for the entire game up to that point. That's realistically a Larian limitation as much as anything else, but in-universe it could also demonstrate Bhaal's general lack of insight into even his favorite spawn.
TLDR: Bhaal already doesn't have a great handle on Durge, despite giving them the urges to guide them to end the world. Even if they do, there's good odds that, in killing all his possible victims and all of his followers, Bhaal would either kill or grievously weaken himself. Unless his goal is going out in one last blaze of glory, his plan for Durge seems like kind of a bad one.
From here on, I go into how all of this incorporates into my specific Durge's story, but there is also a footnote from the Consequences section if you'd like to skip to the end for that (see point one).
