I've actually heard that this is a gang surveillance tactic. The police will act in car pairs to shadow a gang's car from a block over. And not use their sirens or lights to not alert the criminals.
What you describe sounds like an amateur hour Keystone cops level of surveillance. Or some dirty cops doing some shady stuff. A real surveillance would be so much more professional. Depending on the budget/case/interest, they use multiple cars in the pursuit. Some cars are in front, some are behind the subject. They rotate positions so that the same car isn't in the same position all the time. There are so so many other techniques available as well that isn't just conjecture.
Or maybe that's just conjecture.