What do you define as big here? 10mil? 100mil? 1bil? 10bil or more?
Around one billion maybe more, maybe less.
The effect of players on systems should decrease gradually - it already does like you pointed out, but I think it player activity should have less effect on factions on a political level (war, government, system allegiance change…).
Personal playground is about right, I mean why else would you otherwise want to have your own Minor faction installed by FD if it wasn't for the sake of creating your own mark on the Galaxy? …
In my opinion that's the core of the problem since the BGS doesn't look like it was designed for providing that functionality. It is used for that now, and I think it shows that it wasn't initially designed for player factions fighting against each other.
Any change to the BGS should not only take the interests of player groups supporting a faction into account, but also all other players.
A system that affects everybody should be affected by everybody in a similar way. Similar activities should have the same result, no matter how those activities are cashed in.
A lot of this conversation about how the BGS should get affected by players is based on the interests of players supporting factions, how to protect that aspect of the game from getting affected by "non players". Taking one aspect of the BGS and trying to separate the whole BGS from the rest of the player base.
btw: I think it's going to be interesting how squadrons get implemented into the game.