This is not a point of compromise or debate, the deign of the game has already been put in place and you are asking for a fundamental reworking of that design from 'all modes are equal' to a pvp-open centric model where that is the 'favoured' mode and all others are add-ons.
Your 'improvements' to Bgs and PP all boil down to giving a bonus for open and that is the same as giving the other modes a reduction, it is taking away from their game to suit yours.
If Pvp groups are avoiding Power-play Pvp in open, that is a problem of the Pvp groups, not the modes.
See now this is where our points of view differ.
The BGS is great don't get me wrong there, it allows ALL players to influence the system in a meaningful way, very cool, however it is not perfect because there are at least two schools of players here, PvE and PvP.
This is how I perceive the discrepancy in fairness with the system.
PvP players engage in PvP combat to influence the BGS. I call this the PvP component of the BGS (PvPC for easy reference) which is utilised in conjunction with the PvE component of the BgS (PvEC), PvP players will engage in combat with other players in order to hinder influence gains by the opposing faction. Attempting to stop trade, data, UA drops and such also removing players from CZ's, SC, Nav's and Rez's etc, since all of these activities are components of the BGS they are all able to be affected by the PvPC.
PvE players will Solely engage in the PvEC and if doing so in PG or Solo will never be subjected to the PvPC, ensuring that there influence gains will be static with no fluctuation due to limiting themselves to a reduced portion of the Full BGS Mechanics.
I believe this is where things need to be altered. I put forward one suggestion to maybe assist in making this more fair, it may not work but I am at least attempting to find a solution to the problem.
I will touch on PP later. I am due elsewhere for a bit.