Why does a fear - and - punishment approach to supervision usually create a negative, nonproductive environment?

Because productivity directly varies with the suitable work environment , in other words , whenever you need a good product , you have to improve your working environment , here are some positive charecteristics for a work environment:

-Team work.

-Clear goal.

-Motivation.

-Inspiration.

Many other things 

Abour fear , it destorys that suitable environment , destroys concentration , destroys self motivation , it some times gives you a fast result as a supervisor but on the long run it improves the skills of your team in doing wrong things behind your back and widens the distànce between you and them and kills their creativity and self motivation.

I believe, that when a manager uses this technique, isn't sure of himself and his capabilities. He treats the employees like children. This is diminishing and it doesn't allow them to show any anitiative. It's an easier technique than others, which demand by the manager to be a leader for them. To accept their personalities, to help them and extract the best of their knowledge and to inspire them. So, if there is such an awful work environment, I don't think the company or the department could have good business results. 

People resent fear and punishment but adore praise and reward. While fear and punishment are enslaving and create negative emotions, praise and reward are uplifting and instill positive emotions. Fear and punishment create pain while praise and reward create pleasure. Subordinates hate and despise supervisors who inflict pain on them, and love and respect superiors who bestow pleasure on them. This, however, does not mean that a company should not have a code of ethics in place. Neither does it mean that  a company should not have a penal code for misconduct and violations. Companies should resort to negative reinforcement for misbehaving employees, while positive reinforcement should be used for well-behaving, hardworking, and loyal employees. 

After2 things happen you must use the punishment as a tool to keep the performance good:

- If you directed the person/persons to the the right way without positive response.

- If you found the punishment is useful for the person and the company, then you must use it.

Because in many cases there are flaws don't need punishment to be improved, it takes high degrees from blaming the person.

After that, this person will never ever repeat this again, you can add something to all of that.

That person will like the work area so much and like his authority of company.

If a company made that, by that it created a person with high loyalty to his company. 

Mainly fear stops innovation and business improvement. It also freezez effective communication.