Kill count should be awarded to the player that did the most damage to the enemy target
As the title suggests kill count should be given to the player that did the most damage to the enemy target (with exception on minion kills). Assists should go to the people that did lesser damage. Rather than having the guy that got that last hit in.
It would serve to better represent the ones who truly put in the work and end a lot of toxic behavior that stem from people who cite their score as an indication of skill while the people who put in the real work get no credit. It would affect player morale as well.
The score board already shows who did the most damage to you after you have died but it doesn't give the individual who did the most damage that credit.