A crazy idea
What if the gold given on kills was based on the amount of gold people currently had when they died?
Hear me out. I'm talking about the base value of gold given being a % of the gold the dead champion had on them at the time. First blood and bounties would still give extra gold, while dying multiple times in a row would give less. As well as level difference.
In addition, the person who died would LOSE a smaller % of the gold. Say the base % is 10, and a person is sitting around 2k gold. If they were killed for the first time, their killer (assuming same lvl) would gain about 200 gold from the kill and the person who died loses 100 gold (if the % lost is half the % gained). This causes a disparity of 300 gold between the two people.
How could this be better than the current system? Well, it would call for far more critical thinking and analyzing from both people. They would need to consider quite a few things. Such as, how has it been since this person backed? How long has it been since I backed? Are they snowballing hard? How much gold do they need for their next item?
The last one is most interesting. Say you're against riven and she has both components for BC, and you know the total gold to finish the item is 1150, so she doesn't want to back until she has that much gold. The jungler could come help to make it so killing riven will put her further away from reaching that item spike and slow down any snowballing potential.
Personally, I would love this. It would bring higher risk to purchasing the high cost items, since you could potentially lose and give more gold if you die before reaching that gold amount. It would make people think twice about being greedy and overstaying. Make backing while snowballing more worth while, and help people who are behind catch up faster. Most important, it would give cause for much higher levels of decision making from both parties. A person would be more reluctant to want to back if they're ahead in gold than their laner, since they have the potential to give up a higher gold disparity if they died than the enemy. It would give the opposing laner some time to farm, but also miss out on some great opportunities for a massive gold increase if they acted more aggressive.
Just my thoughts. I think it would be really interesting to at least test out.