So why was it removed? I didn't play FE, took some time away between Elemental :war of magic and FE:LH to let stardock try and get things together but sounds like influence might have been a fun aspect, if its anything like Gal Civ's. Generally sad to see things removed from a game to make it easier. While LH is a fun game and I've played it 300 hours worth already I find it somewhat limited and the AI mid to late game somewhat dull and boring as frequently it seems to be a case where every position basically dog piles on you for some coins the main AI offers them to commit suicide, and its one fairly long and dull slog killing them all off for their stupidity.
Your not missing anythin with FE before LH. It was better than WOM but still very boring and just not a fun play. LH is far more fun and better set up than FE ever was. And if you thing the mid to late game of LH is Dull FE makes the LH mid to late game fantastic.
Be happy that they improved it.