well if LASORS is the law (in the UK), then it is ok.
LASORS, of course,
isn't "the law" in the UK. I do hope you know that - and in any case:
as Co-Pilot performing under the supervision of
the Pilot-in-Command the functions and duties of
a Pilot-in-Command (PIC U/S) counted in full.
The functions & duties of a Pilot-in-Command have nothing to do with handling the controls.
so this paragraph (from LASORS) differentiates between PIC U/S and P2 time.
That's because PIC U/S and P2 time are different. You seem to think that "P2" time is time as Pilot Not Flying. The Commander is still the Commander when they are not flying, and a Co-pilot is still a Co-pilot when they are handling - and as such they should be logging Co-pilot time.