Snitches get stitches, there are very few witnesses that will testify in court against a local, so that complicates any kind of law enforcement.
Its a very big leap to assume arresting Brown later on would be without event. For a start it would be a dozen or two cops in full gear and weapons drawn.
Brown wasn't running for exercise, he was avoiding a felony arrest. Five minutes and he would be gone and nobody would have seen anything. Clerk would have refused to identify anyone, and fair chance Brown would move in with another relative in another city and not be found until his next crime spree.
Brown charged at a cop he just beat on, thats nuts and not a good base to consider any kind of change in procedure from. Very few people are that foolish, they stop and surrender without any problems.