Originally Posted by Drip

so, in other words, they were slacking their kills for some reason..

Each EG kill gives all participants a reward (though my sucky luck usually means it's pero), as well as an extra reward to the one that found it.
Additionally, each time you kill an EG, you can encounter another in the gacha, no matter who's EG you killed.

After some SED point, when you know for sure that you will be able to hit the 1000 rank with ease, sharing EG means more rewards are given out, even if less EPs are earned. And it also helps you find more SEG in phase 2, since a friend of yours could kill your EG and go looking for another encounter, even if he already has one running.

But yeah, if your goal is EP, then it's best to share only those you can't kill yourself, or only those that you've already done more than 50% of their health in damage.