I would have zero moral scruples with the genocide of the Black Court, but there might be ramifications similar to the death of the Red Court, which nobody wants.
Agreed on the first part, but not the second. The Black Court has already
been substantially wiped out; that was the whole point of the Stokerlypse. It's been made clear in the books that the only BCVs wandering around are the last remnants of a once-powerful supernatural faction. Now, this may change: while Mavra's ostensible purpose for retrieving Kemmler's last book was defensive (limiting the spread of the knowledge that necromancy could be used against the Black Court, possibly to control BCVs), it's also possible that the book has offensive uses as well (allowing a non-Elder BCV to become an Elder; resurrecting one of the dead Elders; etc.).
The Red Court and the Black Court are similar in that both were wholly evil and properly destroyed. As of, say, Storm Front, though, the Red Court controlled practically all of Central and South America, while the last of the Black Court controlled no significant territory and were kill-on-sight in much of the world. Changes caused a substantial power vacuum (still worth it, IMO); there's no evidence that killing the last of the Black Court would have any sort of similar ripple effects.
In short, I don't believe there are any
in-character moral, legal, or practical objections to Magicpockets' plan worth taking seriously. Out-of-character, it's a different story, unfortunately.
If your players are on the fence, just have some Venator who lost a loved one/family member/childhood friend to the Black Court detail some of their atrocities.
Magicpockets isn't the GM, and due to the backstory he gave, I don't think this would be convincing to the players/characters that need persuading. Also, the GM isn't being reasonable. In a different situation, this is exactly what should have happened, though, I agree.