Logger Heads
The very tone of this debate in itself explains the problem. Common sense cannot be recognised for there MUST be law or a rule or nothing at all. Sometimes this approach is practised as 'micro management'.
DFC
You come to argument therefore expressing the symptoms of the malady of our time. There appears in your reasoning a need to consider a simple but extreme idea of all things only. That is to only consider diametrically opposed positions.
When a PPL holder comes to me for a routine checkout (club check) I recognise that they are qualified to take the aeroplane and act as PIC. The routine check however is one of responsibilty. The club is acting responsibly by having such a rule. The pilot is acting responsibly by subjecting themself to the check. As is agreed, the law doesn't demand this. The check is voluntary. Before the flight however, I make it clear beyond doubt that should I consider it necessary to take command I will do so and they must agree to this.
For this reason the pilot should be PIC unless it is decided that they are to have instruction and that being the purpose of the flight. In such a case it isn't then a checkout at all but an instructional flight.
It is without doubt recognised, just the same, by authorities throughout the world that the most obvious person to undertake a checkout is a qualified Flight Instructor for that is what they are trained to do. They are trained to observe flying skills and in the processes of taking over and handing over control.
I refer again to LASORS section A, appendix B RECORDING OF FLIGHT TIME, Recording of Pilot Function para.1c. 'The holder of an instructor rating may log as pilot-in-command all flight time during which he acts as an instructor in an aeroplane ..........'