Remember the characteristic of the Levites is harsh. One man raped their sister and, as a result, an entire town was slaughtered. Yet, these are the people who are commanded to offer sanctity when there is a deplorable and unfortunate accident. I think it might be that this is more for the benefit of the priest than it is for the manslayer.
It's easy for us to define a person, to characterize and judge them, based upon the single event that we might have heard about them. "That person killed someone." For most of us, that's enough information that we believe we need to know about them to decide that we want nothing to do with them. But, these priests aren't given that option. This person is forced to come and live with them. Suddenly, the priest has to be able to see past the event and get to know the person.
It could be that this exercise is lost among many believers today. We have no cities of refuge. And if we did, we certainly wouldn't be caught there. We'd rather be practiced and knowing just enough about a person to write them off, instead of following the example of our Great High Priest, who loved the whole world so much that He was willing to die for us.