I agree the case was mishandled and this incompetence led to Luke's demise. I think the police did not know what to do. Luke was a 'weak' suspect in terms of physical evidence and this I believe is why they went for profiling. This is not a precise science and profilers often produce conflicting ideas and reports about similar crimes. It is clear that the profile did not fit Luke otherwise they would have used it and called the profiler(s) to testify.
If you have a profile where do you start? Worse still, if none of your potential culprits fits the profile you are left with a blank sheet of paper because you have no idea who it could possibly be or where to start.
If there have been no convictions in the UK of a perpetrator with a similar MO you are lost.
If it is a devious serial killer you can hardly announce this as your finding for the crime.
If the perpetrator gets 'nervy' they may stop temporarily or move to another jurisdiction. (Abroad).
They may have died or committed suicide since the event. They may have been subsequently imprisoned in another country for a similar or unrelated crime.
They may be the type that sees the whole thing as a game of 'catch me if you can', where they become very switched on by this and derive further satisfactions for their efforts in staying one step ahead of the police, above or as well as the thrill or urge to kill.
With the pressure on to provide closure they built a case against Luke, which on cool and calm reflection by those who did not get swept up by the Hysteria at the time looks like a MOJ.
If there has been a conviction in the last 20 years that the Police Scotland now suspect may have been the real culprit they are going to keep schtum.