Powerplay was supposed to be the foreground "political" risk game. The BGS cant be "fixed", it would probably require a fundamental redesign and rebuild to make it the game we ultimately want it to be.
Power-Play got added/patched onto the game after the release of 1.0 - looking at it probably as a panic reaction to the way players manipulate the BGS.
FDev would have to decide what they want the BGS to be. Currently it acts as a basic economical system and a political system.
In my opinion this is one of the main problems.
Separating economical and political (system and station ownership) aspects would solve some of the problems. It would require a political-BGS that handles the factions and has better interaction with power play and the overall political development.
As a next step FDev would have to decide what a faction is. Currently a faction is a bizarre chimera of political party and nation.
How the BGS is manipulated - by value or transaction - is, in my opinion, quite a bit down the list of things that need to get fixed.
And btw, that the BGS is influenced by transaction and not by value (or the other way round) isn't that a much of a problem if things get balanced correctly - an other core problem of FDev. Apparently they come up with "cool" ideas without thinking how that would affect other parts of the game (and other players).
Guess you are right that it's probably an impossible task to fix the BGS.
Could be the case but would be a massive oversight on what players would be interested in.
Wouldn't be the only massive oversight in this game.