I don't know why that doesn't also apply to Quincies.
Pretty much, any soul that had a part of Yhwach infused with will end up going back to Yhwach, removing it from the cycle of going to either Soul Society or Hell. It's why Ichigo's mom didn't end up becoming an Arrancar when Grand Fisher had his mask removed, because her soul "belonged" to Yhwach since her ancestors had a part of Yhwach soul ingrained in them, and so all of their descendants received a small part of that same soul as well (which is why the Quincies are unable to go to Soul Society when they die, because they are the race closest to Yhwach).
The implication is that the Shinigami who had their Zanbaktou's stolen (Hitsugaya, Komamura, Baykuya, Sui Fong) will also end up in Yhwach when they die (and presumably also everyone that is under control by Giselle, so Love, Kensei and Matsumoto are also in line).
As for the Bount ... Kubo is having enough trouble making sense of his own mythology (and he's not doing a good job at it) so I doubt he'd want to complicate things further by including the anime-only arcs in the mix (especially when the Bount arc already contradict who the 11th squad captain was lol).