Basically, not being worth gold is a way of showing that you, as a player, are contributing so little to the match by constantly dying that you become less and less of a target for the enemy team. It's a way to keep a person who's falling behind from continuing to hemorrhage gold to the enemy when they're several levels and a few dozen CS behind, because if they were constantly worth 300 gold then they would constantly be preyed upon as the weak link.
However, getting a kill resets this as it shows that whether through teamwork or smart playing on your own, you've shut down an enemy champion however briefly. Thematically, that's the standpoint. From a mechanical standpoint, it's simply a way of resetting gold so that a player who's falling behind and gets that kill doesn't stay someone who's worth almost nothing while they slowly build back up. It's simply easier to have a reducing amount of gold every time you die successively and then to have it reset once you get a kill.
This is also partially where the idea of not focusing supports comes from, along with them just not being priority targets. In a perfect world, supports only give kills to the other players on a team, as gold is usually much better utilized by more focused combat champions like tanks, bruisers, or carries. As a result, a support would then never get a kill, no matter how many times they died, and while they would be worth less and less gold to the enemy team, they would be keeping up in level and usefulness to their own team by virtue of assists and setting up for winning teamfights through clutch CC abilities and ults. It hurts enemies who try to focus on the weaker targets when they should be worried about other things simply because a support can't really save themselves when collapsed in on. They get no kills, therefor eventually they are worth less and less if they continually die even while giving proper aid to laners.
I don't know the exact numbers, but I've never heard of anyone resetting fully simply by powerfarming or over time. Looks like Axel DC has it all figured out though.