It is not the job of any union to weed out bad employees, it is the unions job to represent all employees not just the good ones. This includes Teachers, Cops, Autoworkers and many more.
The only solution to remedy this is to abolish all unions, good luck with that.
Weeding out bad public employees does represent all employees, including the bad ones.
If you’re a bad cop, you’re in the wrong line of work. You are a danger to yourself and others, physically, or financially, or both. You make everyone, including yourself, suffer through a horrible relationship with the public.
If you’re a bad teacher, you’re in the wrong line of work. Your students will be more likely to commit crimes, including assaulting you or your colleagues. You also make the good teachers waste their time fixing your mistakes.
Autoworkers are private sector, they can have whatever moronic arrangements they want with the employer.