I want to take this and run with it, but... I fear the result will be a wall of text that could be seen from space.
Let me try...
Let's start with the Minor Factions. We've all done something for one of them, somewhere, some time. They're called "Missions". You complete a mission, you get paid. You can some Influence and some Reputation. That faction does too, some partial percentage point of BGS standing, whatever it is.
You keep doing these for the same faction, you eventually become an Ally of that faction.
And then what? Missions pay better, that's about it. Maybe that faction gains enough to try to displace another faction in that system. Yay, now they control the station, and beer is legal again. Let the good times roll. You just won a round of BGS.
It's rubbish. It's the film left at the bottom of a canister of biowaste, after the biowaste has been poured out.
Let's try this again:
You complete a mission for a faction, you gain standing with that faction, that faction gains standing in that system. You keep at it, that faction considers you an Ally.
Now what happens? Well... your "Ally" doesn't permit NPC's belonging to them to try to interdict you. Their enemies on the other hand, might try that much harder. BUT, and this a big one, your Ally might dispatch a ship or two to lend a hand if you find yourself in a sticky situation. Now that Allied status has some meaning. Not much, granted, but anything is better than nothing. Where might this be most helpful? You're sitting out in a vast field of floating rocks, mining your own business, pirates harass you. The local police aren't helping, but a nearby NPC or two, your Allies, see you're having some issues and come to your aid. Awesome. Pirate dispatched, they go back to their business, you resume yours. Just one example.
Now, many minor factions belong to one super power or another. We already know about this, it's how we go about unlocking Rank Locked ships. You complete enough missions, a Navy Mission spawns. Complete that and your Navy Rank increases. Increase it enough, and you unlock a system or a ship.
It works, but it's weak. Let's season it. After completing enough missions for this power-aligned faction, you receive another mission - a Pledge Mission. If you accept it, you've just pledged a Power and joined the ranks of Power Play. You have demonstrated a vested interest in the well-being of a particular faction, they reciprocate by offering the opportunity to "move up in the organization".
Because that's really the biggest point of BGS fiddling anyways - to sway influence for or against a particular power.
It ties everything up into a nice, neat package of sense and logic.
