I've been puzzling over this for a while and I can't really figure out why FFG made this choice.
As it stands, there's very few ways to lose or gain Influence on an individual level. Pretty much all Influence gains and reductions are party wide, which makes a lot of sense; the actions of an warband are going to impact their standing in the world, as an entity. So why isn't Influence a single number affecting the whole party?
In Rogue Trader and Only War, your Influence equivalents are party-wide. Black Crusade is the only other game where they aren't, and it makes a lot more sense there; BC is a game about individual success and gaining the influence of the dark gods yourself. The game tries to encourage a competitive dynamic, so it works.
I can't figure out how it makes sense to have individual Influence values in DH though. Can someone enlighten me? Interested to hear opinions on this.