I don't understand what you're saying - say someone has a busted headlight or is speeding. Police stop the car, which gives them a chance to talk to the person and let them know what's the problem. If it's their headlight - maybe a warning given that the driver promises to change their headlight. If they're speeding the cop can ascertain if the driver is for example sober or not. By this stop the road is indeed policed to be safer.
The being able to stop a serious criminal is just a bonus.
The same safety benefit, without the risk, could be accomplished using some kind of signal with the sirens for "you're getting a ticket", sending a ticket in the mail, and logging it in a database somewhere so the person can look up why they got fined. Warnings could be done in the same way.
If someone is impaired enough to be driving dangerously, police will notice that and should pull them over. I'm talking about the minor infractions which (I presume) make up the majority of stops.
The being able to stop a serious criminal is just a bonus.