I think getting hung up on whether 'professional' or 'amateur' could be a waste of energy.
To me, the point is: was the killer "hired" by someone else who had a motive, or did the killer themselves have the motive.
IMO, anyone down on their luck and willing to kill can be hired to do a job, by someone who doesn't want to be recognized. However, that does mean someone connected to Alistair had ties to some dodgy person or people (if the killer was referred). So police would prioritize looking at any dodgy connections of those around Alistair.
That's not easy to do: police can't easily get into eg. personal or business banking records. On the other hand, since there were at least 2 people involved, they may receive tips, even long after the crime was committed.
Doing the killing for himself, means the killer had some relationship/interaction with Alistair that generated an extreme personal grievance. For that, IMO, police would look at people who were not close, but were mentally disturbed/off. IMO that's actually harder to solve, unless the person did more crimes.
JMO