LOL. I'd quit along with just about every other cop that doesn't drive a desk. Considering that some mope threatened a friend of mine the other day with a lawsuit for "stealing her dignity" by having the temerity to arrest her for shoplifting it would be the only prudent thing to do.
I'd love to see who you could get to do the job under those circumstances. Maybe some parolees could pass the background check. You might want to try hiring some "welfare to work" folks as detectives.
You're missing out on a lot aside from the fact that the NYPD has been losing officers for a number of years. What about all the other duties involved in big city policing? The guys that do background checks on prospective officers don't make arrests and neither do the ones involved in aviation. The harbor unit? Mounted does some great work in crowd control (just ask the anti-war idiots) but they don't often gallop off after burglars. Would you like the bomb squad to chase car thieves or study biological warfare and dirty bombs? We have between 1000-2000 officers every day involved in the War on Terrorism, from investigations to fixed posts in front of high value targets. Don't forget about the staff of the police academy (who serve as field training officers when there is no class in session), the driver training unit and the Manhattan traffic task force. I can't even begin to tell you what a drain useless calls to 911 are on our resources. Do you have any idea how many THOUSANDS of unfounded or deliberately false calls there are every year? How many faulty burglar alarms? How many fender benders that need an accident report?
I have a lot of faith in our detectives, and they do generally get their man when it counts. But what exactly are you going to do when some guy gets robbed on a quiet street and the perp bolts into the subway a minute later and your only description is "a black man with dark clothes"? Theres just not much to go on and if the suspect makes it to the subway, or into a large crowd, he's gone. This isn't Clue and it isn't Colonel Mustard in the living room with the candlestick.