Ok so imagine...

That you're the ADC and You and your support go in on the enemy to kill them. You are about to kill one, you've done so much damage then your support gets the kill. You're like "Ok fine there's another," and you guys go and kill the other enemy but the same thing happens. You, as the adc, might be a little ticked off and the support will be apologizing like crazy. But look no further because i think i have come up with a solution. Instead of whoever gets the last him on the enemy, it's whoever does the most damage to them excluding minions and towers. That way if you're adc and you do 75% damage to the enemy and your support does 25% but the support gets the last hit, you still get the gold for the kill and they get the gold for an assist since you did the most damage.

Edit: Ok how about instead of just changing how the system works, how about the relic shield acts on champions now? However it would just be if the support gets the last hit on them, then the adc would get the kill and gold for it and support would get assist and gold for that. It wouldn't be how it's like on minions where if they're at a certain health. Let me know what you guys think.

Edit2: Ok i just remembered something about kalista and her soulbound. If kalista's soulbound ally gets the last hit on a minion or enemy champion and sentinel is applied, then kalista gets the gold and kill added to her score. So why is it that only kalista has that ability with her soulbound but no one else can have that? https://www.youtube.com/watch?v=XCR-tMpKtt8&t=198 There's the video for proof.