Make the quest support items give more gold through their quests but make support items cost more
I've constantly heard the complaint that "it's not fair that someone who doesn't even farm earns more gold than me and gets to buy cheaper items". It's fair that a support can earn more gold than carries because instead of farming that have to complete a mini challenge. Depending on the item they either have to get in attack range to kill a minion, poke the enemy, or get in attack range to pick up coins.
Plus unlike carries, you can't always be in a situation where you can make use of your quests while carries can just farm all they want. An example being picking a spellthief support where you are losing so your team has to play safe by pushing lanes while farming but you have spellthief stacks that you really want to proc.
Another advantage of what I said in the title is that it could encourage off meta builds more. Maybe instead of having to buy cheap support items as Thresh, you could instead have an easier time building full AD Thresh or full AD Lulu. There might even be more diversity in the bot lane.
If support quests granted more money, they would also allow them to be completed earlier which means they could get sightstone sooner which means bot lane would be less decided by which jungler ganks first or time to prepare for 4 people coming bot and could also result in the game having less snowball.
I don't have a good idea of how much more the support items should cost but maybe they could all cost 200 gold more. Maybe someone could help come up with a good idea in the comments of how much more gold the support quests should provide and how much more gold support items should cost.