(Major spoilers here.)

The following is probably obvious, but once you start following the dots at the end of the show it's clear that what happened with the queerrats is almost inevitable. Right now I feel like laying out why this is so.

A core ingredient in the precarious stability of Cantus humans is death feedback, which makes it so that almost no Cantus human can use Cantus on another human to any dangerous degree. In its flashbacks to history the show gave us a fair number of examples of what happened without this precaution (and then the false minashiro explained it). But death feedback presents a problem for Cantus humans as they interact with regular humans, especially after the history we were shown. Put simply, Cantus is what keeps Cantus humans safe from humans but death feedback means Cantus humans can't actually use it; regular humans are thus free to come after Cantus humans with everything from sharp rocks to firearms and kill them all.

This gave Cantus humans not very many options. They could completely wipe out regular humans, they could somehow completely isolate themselves from regular humans (and make a very big bet on that isolation lasting forever), or they could somehow make it possible to safely use Cantus on regular humans without invoking death feedback. The latter is what they did: they made regular humans non-human enough that they would not trigger death feedback (or at least that they would not usually trigger death feedback; as we saw during the show, killing queerrats can still trigger it under some circumstances). Cantus humans still needed to keep an eye on queerrats, especially initially; as Squealer showed, Cantus is not guaranteed protection in many ways.

(I suppose they could also somehow make it so that regular humans couldn't attack Cantus humans, but I don't think that that's a reliable protection. Note that death feedback itself is not reliable, cf fiends.)

I don't think that the Cantus humans initially warped humans into queerrats to have slaves. I think that was just a side effect of having queerrats around and keeping an eye on them.

I see the biology of queerrat queens as a measure to make it easier to control and limit queerrats. Queerrat queens are implied to be large and mostly immobile, and they are the only breeding source of queerrats. This makes it much easier to keep track of them and much easier to eliminate rogue colonies (just kill the queen and ignore everything else) and control the spread of colonies. Cantus humans were undoubtedly already very familiar with how hard it is to control the population of people who can breed freely and widely.