I think that you will find that in the cases where the check is done by a pilot who does not hold a valid instructor rating then the pilot who is being checked can not log any time but can only record the take-off and landings they completed as sole manipulator of the controls.
If the person being checked out can't log the hours, and the person who checks the other guy out only holds a PPL and never touches the controls or makes any decision, just observes, who gets to log P1 then?
Oh, and if the designated check pilot only holds a PPL, and has to be PIC for the flight (by your rules), this also means he's got to pay at least an equal share of the costs of that flight. I doubt somehow that you get many PPLs volunteering then as check pilot.
I am surprised to see that there is no general objection to having to complete a 28 day check the only objection being to having to log dual time for the 10 to 40 minutes is takes to complete such a check.
Well, it's not exactly the subject of the thread, but just for the record, I object. I would rather see a more flexible approach where you need a 28 day check if you hold less than 100 hours P1 or so, a 60-day check if you have less than 200 hours or so, and no additional checks above and beyond what the law requires above 200 hours P1. Or something along those lines. You may even throw in an "hours on type"/"landings on type" criteria for all I care. But I somehow trust the more experienced pilots to be able to make a fair assessment about their own proficiency, their mission and the circumstances, and not to take unnecessary risks.