In my opinion the faction influence feature is a very interesting feature that is under developed in ES. On top of the effects that it already has it would be interesting that it would influence the general happiness of enemy factions as for example when one enemy world is completely surrounded by another faction influence. That it would have consequences in diplomacy and that if a world is surrounded by another faction influence it would slip its allegiance to that faction. in between other effects.

Agreed. It works well in some other 4x games. You should be able to take over a system peacefully, without having to pay outright for it!!