The question is would your players loot corpses if it was a choice between that and death, or do you just have such high turnover or so little combat that it doesn't matter ?
If they were caught in a prison and killed a guard and then needed weapon to get free, yes.
Otherwise, they take their time, they planify their mission, they develop and make contacts, and get the gear they need by doing jobs for other people that have the power and influence to give them what they want. In the end, influence is an abstract value. They make a test, succeed, they get to meet the good guy that can help them, sometime in exchange of something, then they get their power sword.
But in my games, anyways, gear stays pretty low, since high gear means being targeted by everyone that think you could be an ennemy.
That's a complicated conjecture. The game comes from the tabletop and the novels. I don't run pure 'purge missions' very often, but the poor social rules and the massive amount of attention paid to weapons, armor, and combat in general doesn't really support that DH was intended to be something like Trail of Cthulhu
Combat is what is more complicated. It doesn't mean that because it has more rules to fit it, it means that the game is mainly combat.
There are enough rules and contexts to make social a greater thing. In the end, tests vs tests are supposed to give results in a situation where tests are needed. It's not necessarily supposed to be a "Oh, I've got a good role, end of the social encounter".
Harlock Legacy, one of the greatest premade campaign, had not lots of fighting in it. Still, it represents in my opinion the greatest DH adventure and what the game is supposed to be like.
For the loot, there are many ways to help with this, I'll write something tomorrow