I had a rather funny mishap with the easily aggroed NCPD.
I had just started the side mission "Burning Desire", which automatically spawns V's car. I got in the car, and just as the mission giver Jesse Johnson had entered the car, that's when a NCPD car rear-ended me, then opened fire. Within seconds, Jesse got back out of V's car and exploded. Mission failure, thanks to the hyper-aggressive NCPD, heh.
Anyway, while the new police system can be sometimes game breaking, I don't find it overly immersion breaking. It has already been established that many officers on the NCPD force are corrupt buttholes who take bribes from the rich and gangs, while taking out their inflated egos on V and other innocent civilians.