Yeah that's what happens in practice, but it's not a good use of police resources. Road policing should be focused on keeping the roads safe, not fishing for unrelated crimes. The cost-benefit for society and the police on these stops is terrible.
The being able to stop a serious criminal is just a bonus.
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.