Living in a society where the police had no discretion and, instead, had to enforce every law to the letter would have its good points and its bad points. On the good side, there would be little or no doubt about the point at which you would be judged to have broken the law. There would also be no feeling that the law was being applied unfairly. On the bad side, the system would become more impersonal and incidents that felt very unjust would surely occur with greater frequency.
In our current system, it is not always easy to know how far you can bend the law before you are liable to get in trouble. The clearest example of this is in traffic laws. It is not common for the police to stop people who are, for example, going 5 miles per hour over the speed limit on the freeway. But it is possible and it causes there to be an element of doubt in a person’s mind. The element of doubt also allows for the perception of unfairness. You might get pulled over for going 5 miles over the limit and feel as if the police are persecuting you because they would not have stopped someone else for doing the same. This is particularly a problem among members of racial minorities who tend to feel that they are getting singled out for poor treatment. Neither of these types of situation would happen if police had no discretion. There might also be less crime as people would know that they could not get away with anything.
On the other side, a system with no flexibility will often seem unjust. For example, going by the strict letter of the law, the police might have to arrest and detain a 10 year old who shoplifted a piece of candy. In the current system, they might bring the child home and talk to the parent without actually putting the child into the juvenile justice system. This sort of seemingly just act would be impossible.
Thus, there would clearly be good and bad aspects to life in such a situation.