Anyone using P1s has never read LASORS
P1S has been used since long before LASORS was invented. LASORS is only a "guidance" document that has no formal status whatsoever. "P1S" has been an abbreviation for "PIC U/S" for many years, and as you said yourself:
You can log anything you like in a log book
The only legal requirements for logging are those in Art 79.