No doubt it's frustrating at best and heartbreaking for the families. And I'm sure not all agencies are as competent and honest as I'm making it sound
One thing with Denim is that ruleouts are usually a lot faster than confirmation. Especially if the missing person or the UID don't have direct relatives and they have to track down several cousins to get enough DNA information to make an identity certain.
If there is a cold case unit, then yes, it usually operates separately. Some such units are fully staffed with adequate budget (the recent Virginia project to go through all their UIDs and missing people and investigate all matches, for instance) but usually they only work on a subset of cases. If they're working with retired staff (who are often part time) or people giving their extra time, progress will be slow because of the limited hours. But most missing persons cases are mixed in with all the other everyday stuff and don't get as much attention.
UID cases in many states aren't even handled by regular police or sheriff's offices; they're investigated by the medical examiner's office. There's a shortage of qualified MEs nationwide right now, and with the opiate and meth epidemics, many ME offices are swamped with everyday work.
I've been trying to poke my local legislators to increase state funding for DNA testing and cold case investigation, but there are so many other needs. It's sad.