I'm with UMW on this - I like the trait system.
If you do go with your decision, I'd make sure that they can still gain no more than one trait per game.
We decided to award killing and injuring by introducing a 'Deading League' to our campaign:
3 points for deading an enemy, 1 for an injury that removes a foe from the fight. 5 points for accidentally deading a gangmate (excluding yourself). A ganger will only be added to the table when they score above 0. No points are gained for killing hostages.
Having your gang member top the Deading League adds +1 to their personal rep. This is lost as soon as they are toppled. If two or more gang members occupy the top spot, nobody gains the bonus. Gang members are not removed from the league when deaded, but it does become harder for them to maintain their lead.
It helps that I keep battle reports of each fight to keep track. I think it will cause another level of ugly rivalry and mud-slinging. We're only able to play in fits and starts, so we keep things ticking over on a forum.