Killing on suspicion is the entire purpose of the gamemode. If you're only going to kill on absolute proof, the innocents will lose every round. Because even witnessing a murder isn't absolute proof. Innocents can do everything the mafia can.
There are many things I've killed innocents for simply because they shouldn't be doing it:
-Using body bags
-Finishing off unconscious people.
-Throwing unconscious people around.
-Constantly trying to get out of view.
-Following a single person out of the scene.
In a server that had a 'karma' system, I've stayed well over 100 points by playing like this.
Though killing for an item they had was never something I've done.
In my opinion, the 'karma' system should be in place. This sorts the suspicion kills from the RDMers. Necessary punishments for people who drop to a certain score. Like limiting their starting items to weaker weapons and eventually nothing that does damage.
How it should work:
All karma earned/lost during the round will not be given until the round ends, and is shown by score in the f2 window.
Innocent vs. Mafia kill = 3 points.
With the balance of the game, there are far more innocents than there are mafia. Killing a mafia is an accomplishment. However, can't reward too much, as an RDMer might gain more than lost this way. This gives good players 3 mistakes to each good play, which is pretty comfortable.
Innocent vs. Innocent kill = -1 point.
Of course, the goal of the game is to kill suspicious people who may be mafia. They shouldn't be punished harshly just because some other player was being an idiot. However, an idiot will still rack up that negative karma pretty quickly if everyone's a target.
Mafia vs. Mafia kill = -5 points.
There should be no reason to ever kill a fellow mafia. Ever. Your job is to kill the innocents. You know who is innocent or not. With the exception of this one broken server I played on where mafia couldn't see names/teams till they took damage.
Mafia vs Innocent kill = 0 points.
It's an easy objective. If an RDMer was awarded from just picking off all the innocents and then also picking off all the innocents when the opposite role, they'll never go negative. The goal here isn't to reward good players, but to punish bad ones.