P1S would seem eminently sensible for someone to log if they are being supervised by an instructor. Quite why the rules (apparently) say otherwise defeats me.
Logging PICUS for a successful Flight Test is, I believe, a UK peculiarity - The rest of EASA land only using it for Multi Pilot roles and some flying during integrated courses.
In Single Pilot Flying: If the 'Checkee' is logging PICUS then they are
not a student so the other pilot, although PIC, could not claim it as an
Instructional Flight (so no need to be an Instructor at all). Instructors
do need to have logged a certain amount of instructional hours and
if it wasn't an instructional flight then (in all likelihood) the PIC would
not legally be allowed to be paid.