I was a 12 year old resident of new york city when that movie came out in 1981.
At the time, the city was really crumbling and the crime rate had been getting worse year after year and would continue to do so. You were either a crime victim or you knew someone who was a victim.
The local politicians were absolutely useless as they were soft on crime (as well as the judges they appointed or were voted in). They were tone deaf to the complaints about crime and would just shrug their shoulders and say that the crime rate is normal for a big city and if it werent for them, it would be much higher.
So, the premise of the island of Manhattan being walled off, and turned into a giant maximum security prison with mine fields on the bridges didnt seem so far fetched. It actually looked like a plausible, sound idea and was thought that there was a possibility the way things were going, this was where Manhattan could be headed. Many new yorkers, myself included, would have welcomed such a development.