Way way back (1960/70s), one had to have a separate licence (a mobile licence, costing two quid, no less) in order to legally operate /M. In those days, /M specifically meant operating from a car or a bike that was being driven/ridden at the time. You could operate from a car that was parked up and sign /P, thus not needing a separate /M licence. Some of us operated /P from lots of different places during the course of a QSO on some occasions. £2 was a lot of money in those days!
/P back then meant operating from a location that did not have a postal address. /A was used for operations from a different location to that printed on your licence WITH a postal address. To operate /A you had to give prior notification to the authorities. It was a simple suffix system, entirely understandable and quite logical.
Then they did away with /A, because of the hassle (to the authorities) of all that notification business, and the confusion began to set in. And radios became small enough that you could walk around with them so yet further confusion arose regarding the correct suffix to use.
/P has NEVER, in the 40+ years that I have been licensed, meant operating pedestrian portable. It may have been deemed to INCLUDE that mode of operation (because of the separate /M licence requirement) but it was not exclusive to it. For example, all field day operations are and always have been /P.
Nowadays the licensing authorities have washed their hands of the whole suffix business and we are left to do our own thing. That I think is a great shame. My opinion, which is worth exactly what you paid for it, is that /P is the most appropriate suffix for all SOTA operations, including when you are talking and hiking at the same time. Definitely /P for when you’re operating from the summit. This strategy is most in keeping with historical precedent and is, in my opinion, also the most logical.