No, it's a good idea. BGS may have originally be intended for, well background, but its manipulation is one of the things that keep players playing after they have grinded everything. It could use some love. Other thing is that some players have accumulated many billions of credits and have nothing to use them on. Investing to a faction to generate certain types of missions in a specific system would be a nice way to gamble with those billions and have a bit more levers to manipulate factions without really controlling them.
But again, that's a totally different thing to literal faction management.
I don't like the idea of making factions generate certain mission types, because it's the
background sim. You can already control the mission types by influencing state. mechanics to Incentivise players to undertake certain activities would be great. Direct control would be game-breaking. Those interactions
must be indirect otherwise it's not the background sim, it's the "foreground sim", and FD have stated they've failed at their job if that's what it becomes.
The other issue is that there is no chain of command/control. Anyone can pledge to and support whoever they like, and you can't deconflict that; that's fundamental to the nature of being an independent Pilot's Federation commander. Giving control over a faction to anyone fundamentally changes what you are, and your representation in the game.
Again... letting players influence factions by incentivising player activity which supports or detracts from a particular faction; great, awesome, all for it. Controlling how factions behave/operate/function, no way. That goes completely against the nature of the game, and being a member of the Pilot's Federation (i.e game mechanics, and lore).