Problem is that cannon minions are half the battle in all the lanes. It takes a decent amount of thought (particularly if you get bottom role as a fill or secondary) to avoid what is a primary target in both Top and Mid, and even Bottom in most games. On top of that, even Supports make mistakes sometimes, including trying to harass an enemy, killing a minion instead, and losing the Relic charge they planned to have for Cannon. This means an ADC has to micromanage even more on checking how many orbs are floating around their ally.
Not saying it's at all right to knowingly hold your ally from minions, but in normal scenarios, accidents happen. There's a lot going on in bottom in most games.
I kinda feel like the micromanaging is more than it's worth. I feel like it might be beneficial to drop the passive gold income altogether on the Relic line and add a mechanic where it awards gold to make up the difference if a non-cannon is taken (only to the support). There's already a heavy disadvantage to Relic players vs. Spellthief players (or Klepto Ezreals) in that the minion collection creates mandatory vulnerability periods. It would be nice to at least not make it that obvious when those are, and double bonus for also reducing the ADC's burden on reserving key Cannon CS for their supports. I just don't think that's a fun mechanic to work around.
As a backup plan, I don't think it would hurt to make cannons significantly easier to grab for supports lategame, either a much larger HP threshold for instakill, or even a CS stealing mechanic if it's hit with a melee basic attack and an ally deals the killing blow (not a true steal, just make sure both bottom laners get their piece).