Do the quincies want that? To me, Haschwalth's comment about Uryuu learning the truth about Yhwach's intentions is a red flag warning me away from assuming the Stern Ritter know Yhwach's true intentions, especially since they didn't know anything about Uryuu, they don't know why Yhwach's made him his successor and they don't understand why Haschwalth isn't challenging it.
So, what are the quincies fighting for? We don't actually know. What about Yhwach then. What's he fighting for? Well, we don't really know that either. However, considering that he's been talking about reclaiming the world, he doesn't seem interested in destroying existence so much as radically altering the existence everyone is currently familiar with.
Destroying the existence someone knows and destroying existence itself might be the same thing to the affected individual, but it's not the same thing on a metaphysical level.
The issue we have is, of course, that existence itself is threatened and there's an indication that the quincies have historically struggled to comprehend this very big picture - the reason Urahara offered is that it's because they have a very human point of view, so they only see a narrow point of view. Aizen babbled on about this idea of humans only being able to see the reality they can comprehend as well, so there's a connection here between Urahara and Aizen's philosophies... and we don't know how right or accurate either of them are.
As readers, we know there are tears beginning to appear in Karakura Town and that Mayuri had to rebalance the soul counts on the two sides. What we don't know is how well known this is among the quincies themselves. Do they know what their activities have been doing? The extent of this damage wasn't exactly common knowledge among the shinigami either, even the captains didn't seem to know how urgently Mayuri was acting or what lengths he was going to - even the captain-commander himself didn't know until Kira began to get suspicious, raised his concerns and led to Yamamoto questioning Mayuri.
So, if this isn't necessarily common knowledge among the shinigami who make it their business to be aware of this subject, is it common knowledge among the quincies who may have their eye fixed on a different ball entirely? For Yhwach to be unaware is, in my personal opinion, unlikely and it's probably something he's counting on. At least, it wouldn't surprise me if that was the case. However, the quincies as a whole? They don't really seem to be within Yhwach's loop. If anything, Yhwach seems to be using the quincies as fodder or stepping stones to achieve something he's not admitting to them he's after.
I therefore question how we should be viewing the quincies as a group even if we should be regarding certain individuals as evil. I know how Shutara worded things, but the Royal Guard seems to have its own agenda and, as usual, Ichigo appears to be the pawn no-one wants to give too much information to.