I would imagine one of the primary reasons for not reporting to the police in the USA is to avoid reporting to insurance companies. A claim makes one's premiums go up, often higher than it would take to amicably settle the issue between the drivers.
Note: I'm not commenting on the legality of such an approach, which varies by local law and the severity of the crash.
Note: I'm not commenting on the legality of such an approach, which varies by local law and the severity of the crash.