I do not believe there are any downsides to having a DNA database, and it would make an incredible difference in solving crimes and stopping violent criminals and keeping them off the streets. If only people who have been arrested before have DNA in the system, then the really clever criminals who know how not to get caught stay out of the system and remain harder to catch.
I think it make sense to have DNA database for many reason. First of all this would ensure that we have the perfect record of every person. Having this record would be more easier to catch criminals and also it would bring down crime. Lets a crime scene didin't have any finger prints but a ciminal's hair fell on the crime scene, then we can trace the DNA from that hair and catch the criminal