In my experience (I've had six student teachers in 20 years), there is not a lot of time or energy that goes into candidate placement for student teaching assignments. Schools of education at the universities have a pretty large number to place, and in competition with all of the other colleges, so they are looking for a slot, mostly. With luck, they will choose a good match for a school, but I don't think any consideration is given to the right teacher. If at all, the building principal might make a suggestion when it comes to that.
As a teacher, it has been frustrating to me at times to work with a student teacher who isn't a good fit for me, but I try to look at it just as there are students who aren't a good fit for me. They still need to learn, and this is where they have been placed. I try to work with them and train them to the best of my ability, hopefully getting something out of it myself in the process.