They don't stop a specific crime in that moment, but given that criminals tend to commit multiple crimes, being able to identify and remove a criminal from the streets, seems to logically prevent the other crimes that criminal is likely to commit from happening.

It's the basis of the broken windows policing concept. If you catch the guy that broke the window and take him in, chances are it's not his first crime and it is likely that he or she can be linked to other crimes that are being investigated and taking him or her off the streets means they won't commit more crimes.