I think you are struggling to separate the rules that apply to airline training and the rules that apply to flight instruction in the classic sense.
I am not struggling with anything thank you, the ANO and LASORS are very clear and apply to all types of flying, they do not show P1/s
nor do they say or imply that instruction cannot be given by a pilot who does not have an instructors rating.
An instructors rating is only required when instruction is given for the purpose of the grant/renewal of a licence or rating.
You need to understand the regulations and comment on the regulations not what you would like them to say to agree with your argument, (God help the IMC rating)