As long as there is competition and direct opposition, it's PvP. There are plenty of games where they have modes where opposing teams fight in PvE fashion that creates obstacle of the opposing team. Tera for one has exactly this sort of mechanic where the more PvE mobs one team defeats, the more difficult the opposing team has it in PvE. There is no Pk happening, but it's a PvP mechanic regardless because the final results and what matters for the said mechanic is PvP, not PvE. If we are all fighting in one faction against say thargoid, then it's PvE. But it's clearly not the case.
I actually don't disagree with you here - playing the PvE PP mechanics to oppose other players doing the same thing is a form of PvP. However, it is not an overt form of PvP, it is hidden from view in many ways, apart from monitoring the stats and positions of each power from one cyce to the next. It doesn't even compare, in my opinion, to even playing chess or any board game as a form of PvP, let alone Elite. You can participate in PP and NEVER ever see another player, irrespective of the mode one players. When I dabbled in PP, I played it for weeks - principally in open - and never saw more than a handful of players the whole time - and then only when they were in stations. Simply due to the matchmaking I would expect. Not exactly significantly different to playing PP in solo or a private group, apart from when I was docked. So why incentivise playing it in open when playing it in open, for many (most?), will outwardly be no different to playing it in solo or a private group anyway?
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Furthermore, by far and away the majority of time people discuss PvP, here or in any other game, they are discussing overt, player-on-player, direct combat, NOT something indirect like PP. While PP has PvP undertones as you describe, for all intents and purposes all most people see are the PvE mechanics overlying that. So as far as most people will be concerned it's PvE, especially as combative PvP - the very thing MOST people envisage when someone talks about PvP - has actually very little to do with PP in the majority of circumstances.