I'm having this same issue constantly in version 0.4.4 (newest). Rarely does a suspect ever fire a weapon at me or any other police officers (finally got a suspect to shoot first when I arrived to a 24/7 market and ran inside while the suspect was still holding up the clerk). Even Code 3s and “code 99s” as stated by the female police dispatcher when “all police officers are advised to respond due to shots fired.” I get to the scene and nobody is shooting whether or not the persuit is taking place on foot or in vehicle.
A side not would be that "takedowns" are extremely easy. You hold E when pointing a weapon and they give up 100% of the time. LCPDFR in GTA IV was almost more dynamic... but considering no one else is complaining about this I'm wondering if it's user error??