I am very concerned about labour rights, as that will be very important in a world of ever-fewer jobs with more competition for those jobs, for the students when they grow up, and for now, when their parents need jobs to support their family.
If students can get teachers fired with just an accusation,
* The students will end up with a fragmented education from a chain of supply teachers and replacements.
* Teachers will have to pander to students even more than they already do, for fear that a disgruntled student will decide to cry wolf. Lessons will focus on fun, not education, and teachers will be unable to stop students from disrupting class.
The comparison to a trader or hedge fund manager doesn't stand, as the market cannot decide to deliberately move against him out of spite, a need for power, or boredom.
[EDIT: Forgot to mention that private companies are more motivated to care about the product. Public school administrators would be more concerned about 'liability' and eliminating a source of 'hassle', than with the quality of the product. There's little incentive for them to work to keep a good teacher who's been unfairly accused.
The comparison to programmers is also not appropriate, for those same reasons.]