Ok what about this middle way solution:
Systems with PMF in it bgs works in open only. While systems with no PMF factions present can still be affected by PG/Solo. Or somekinda player group decission if they wanna keep old bgs mechanic in their systems or not.
And this is just a reyally I did not think on this at all...
So your faction obviously only would be affected by Open and PvP stuff, just like you suggested..
My faction, would use the oldy style BGS
Explain how these two faction can have a conflict?
I do not play in open or even on your platform, so who would you kill then? and why shoudl you be able to have influence over my faction that allows the Solo/PG option
Since all of my actions would be done in Solo/PG then why should Open stuff from a faction that is rejects Solo/PG stuff affect my Faction?
Just pulling suggestion out like this without even trying to explain how it should work when two conflicting set of rules collide like this is quite telling about how much though have been placed on this. Not understanding what the problem is, and then applying your own wanted gameplay to be the main gameplay as the desired goal is not a good recipe for good solutions.
And lets not forget about the really big elephant in this room, PvP is something most players do not engage with. ie, they do not go looking for PvP interaction, instead most players avoid PvP interactions and prefer to change instance, move to another system, instead of engaging in PvP. And taking this into consideration, then it is quite clear that promoting PvP for BGS is very unlikely. FDev have already told about the most preferred game mode and player engaged in PvP, and failing to understand what FDev said in those statements, is telling about the motives behind these kind of suggestions, a minority group of players want to force other players to become their content, and if that ever happens, the end result would most likely be an exodus of many players, since those players do not enjoy PvP and being forced to do PvP stuff would simply make this game unappealing to them.