I didn't say it was a ban; they were to be unnecessary because the people were to be law enforcement. There were no police for nearly 100 years after the Constitution was ratified.
No. Philadelphia Police Department was established in 1751. NYPD was established from the remains of several prior police agencies in 1845. Boston PD started in 1838. If you want to include the predecessor ‘watch’ organization or town guards (which was also pretty much all they had in most European countries at the time too), policing in America goes back to 1636.