I'd say for the most part what you are saying is true, but a couple months back Privateer's Alliance (PA) got into a BGS war with Mobius (the actual player group, not the whole private group that people play in) in Colonia. Having never been involved in one, it sounded like it had the promise to be an interesting undertaking. Both sides knew it was happening, all the PA ships flew with PA tags so we would be obvious to other players. Through various discords/inara, we knew who most of the Mobius players were.
Not surprisingly, the only players we would run into in open were other PA ships (for the most part). Pop into the Mobius private group and we would see the Mobius players going about doing whatever their "war" activities were.
The only time I ran into a Mobius player in open, was sitting in stations. They never moved and were essentially just blocking landing pads, the medium pad on outposts. All's far in love and war I guess.
And I fully understand PVP isn't the end all be all for BGS war stuff. But if I'm in a PVP capable ship, in a Mobius controlled system killing cops to reduce influence, and I run into an enemy running missions, killing them is going to be helpful. It would also have made it more interesting for when I'm running missions in my Asp to actually run into another player intent on stopping me.
The whole experience was completely unrewarding and was the thing that got me to stop playing Elite for a while (3.0 looks like it might get me back). Being in a war to some invisible hand is beyond me for a game mechanic, but I get that is how it is designed.
I also have hopes, albeit low, for Frontier to add some meaningful PVP mechanic.
Oh, and Mobius won the war