In my opinion, police dogs, in the US at least, are a vestigial cultural holdover from law enforcement's slave catching past. There isn't really a good tactical reason to be using them that couldn't be performed by other equipment. They are unreliable, expensive, and get shot surprisingly often. If you really interrogated why they still use attack dogs, their answer would be that those people are scared of them.
Other than that, scenthounds are just probable cause generators which are all probably trained to alert on command.