I say force them to actually play the game to get their pay day.
My only hesitation with your suggestion is it's impact on the new players. If it was simply settlements governed that determine the payout rate for minerals, the current game leaders would only be fortified in their position, while the new and lower-end players would be penalized as the only way they would have to reliable take over settlements would be STO cards.
Maybe we could introduce a random mechanism that would occasionally oust standing governors. Or do something like we are planning on Phobos, where you are required to regularly visit your holdings to retain them.