I have a better idea: why don't we just buy penthouse suites overlooking New York City and keep them there? Why not just let them go?
Why are innocent people executed?
Why? Because when a murder or violent situation comes up, the police don't go knocking door to door to try and find the criminal. They have a pretty good idea of who they are looking for because typically, criminals develop a pattern and detectives are able to narrow it down to the likely suspects in a city or area.
In other words, when police have an unsolved murder, they don't go to Joe Shmoes' house while he's planting tomatoes with his 12 year old son and haul him off to jail.
Using whatever information they have available, they create a list of possible suspects, and then proceed with the process of elimination. Then see if their evidence matches the suspects they narrowed it down to.
A few years ago somebody was going around robbing churches on our area and getting away with it. The police knew this was no amateur because he left no clues.
Then one veteran officer remembered a similar situation 25 years earlier, and they dug up the case. It was a long shot, but they found the guy (still living in the area) and used him as a suspect. They busted him, and the judge sentenced him to 5 years in prison.