I think the problem with Sabbat campaign in VtMB would have been that since Sabbat is de facto in a state of war with the Anarchs, the Kuei-Jin, and the Camarilla over the Free State. They'd have had to make a completely parallel storyline if you join Sabbat (not the least because things like Vaulderie are kinda difficult to factor in otherwise). I think they did a fairly decent job with what limited use of the Sabbat they did, having a bunch of power-tripping shovelheads who don't have much of a brain or understanding why they're doing something besides a very banal criminal viewpoint of just "claiming turf and doing whatever I want", which was then juxtaposed by the Sabbat Elder Andrei who is in on the real case of things, and is in his own viewpoint on a religious mission to stop the apocalypse.
I think Sabbat would have required even more work than Giovanni since it takes considerably more effort to establish how Sabbat operates and what its inner workings are, or how they evolved from original Anarchs. After all, Giovanni just takes the same mafia shtick Camarilla runs with. Sabbat is a group of politically zealous Catholic anarchist occasional satanist crusader nomad cell organization with multiple competing ideological factions and a leadership that's just as eager to backstab each other as the one in Camarilla.
I don't think VtMB would have done WoD as much justice as it did if you'd have been some kind of Inconnu tourist taking a full tour with all the organizations in LA, rather than a Camarilla mook->handyman. Interacting with that pompous oaf Lacroix was always fun.