Here in the UK they would certainly take on "trace" work, ie finding mispers, but it's usually in cases where the police would not get involved. The police obviously investigate missing kids and vulnerable adults, and no doubt Corrie's case because of his military status. But finding longlost aunties, adult children and suchlike, no. That's really where a PI is involved. That and finding absconding debtors.
Correct on confidential records and breaking the law. Actually the use of trackers is perfectly legal in the UK providing you don't break any laws in doing so. So you can attach a tracker underneath a vehicle but cannot break into it to put the tracker inside. In some respects using trackers as part of surveillance is preferable to following someone directly by vehicle - less chance of an accident or being spotted and no having to break the speed limit to keep up if the target does.
I would guess they will have to reinvent the wheel and go over much of the same ground as the police already have. They may uncover information that the police have but haven't shared with the family. Then again they may not.