The amount of kills you have don't affect your rewards and the people who just run past everything make a good point, why kill everything if it doesn't keep you from advancing? Maybe if Bungie got creative for once, the person with the highest amount of kills could have a better chance of a catalyst dropping or just getting better gear, maybe a better chance of an exotic that will actually help your light level go up.
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See, the thing is that personally, i have not once seen the "run past everything" tactic work. All that happens is the one person runs ahead, dies before reaching a checkpoint, respawns, and repeats it. Meanwhile me and the other player are killing the enemies and actually moving through the level