It's not that simple. Yes, there are times where it can become too high risk (places with lots of pedestrians), but generally it makes a lot of sense to stay in chase, especially for someone suspected of a violent crime.

1) they could be in a stolen car, which is quite often the case when people are fleeing from police. If you let them flee, you will never know who the suspect is and you'll never catch them after they dump the car.

2) a lot of people who flee already have a warrant out for their arrest, so "tracking them down later" might not be as easy as it seems.

3) let's imagine the guy has an illegally obtained modified fully-automatic AR-15 in the car. If the cop doesn't continue the chase, the guy can just wait till the cops disengage and stash the weapon somewhere before being picked up later.

4) a lot more criminals would flee from police when they are doing illegal things and/or have contraband on them. Criminals would start to learn that they are able to easily lose the cops and hide their contraband and other evidence of criminality.