Do you sign for the aircraft when you go flying Step? I usually don't.
With every club I have either flown at or instructed at then what SHOULD happen is that the captain signs for the aircraft before flight then completes the times AFTER the flight. I know that sometimes this doesn't happen.
I state that the "other" pilot is PIC, and I will brief, then intercede, only as required, and that won't relieve them of PIC duties
Except that as a "passenger" you are not legally entitled to relieve them of their PIC (or any other) duties.
I wonder if its just remotely possible that for the large majority of these flights, both of the pilots log P1 time and that nobody actually cares, nobody actually checks, and that for an uneventful flight it doesn't even actually matter.
But in the event of an eventful flight it will definitely matter.
Tech log is a fair point - but retrospective
With this retrospective filling in of the tech log lets see who rushes to fill it in after an incident. The instructor who says that you were PIC or the pilot under check who says that you were the instructor therefore you were responsible. I bet I wouldn't get killed in the rush!
This may be all pedantic but when the sh*t hits the fan then it will most definitely matter. Ambulance chasing lawyers will get involved.