I think one of their worries in this matter is that sooner or later some individual's preference or opinion or personal choice will come into the evaluation of the teachers, and that arbitrariness will enter the equation, and then chaos will ensue.
I'll concede that someone's opinion will enter into it. I'll concede that sooner or later someone will not receive as much as they think they deserve and will bring up charges of favoritism.
I won't concede that chaos will ensue. A hundred years ago someone preferred the older geezer teacher to the callow young pretty teacher and kept him on even though the younger teacher was much beloved by her students. People shrugged and life went on, and the young teacher found herself a job a year later in another town. See how that works?
I strongly recommend reading Marva Collins' Way. The TV movie was striking but as you'd expect, it says a lot less. There is so much to learn from her experiences as a Chicago school teacher. Reading this book taught me a lot about teaching, and I repeat her stories to other people all the time.
Return to Excellence in Education&Quality in our Classrooms Marva Collins Way
Here is a link to the book I believe I'm thinking of:
Sowell is a fascinating writer; I've enjoyed all the books by him that I've read. Applied Economics is probably the next one.