Gold income items, Are they actually worth upgrading?

So recently i took another look at the 3 support income items, and the more i looked the more i started to really wonder if they are strong enough to justify getting the upgrades, tier 2, for them in the early game. The more i played the more i felt like the Spelltheif's edge upgrade really doesn't get much in comparison to the Relic shield, or the ancient coin. And over all that the Relic shield gives the most bang for your buck.

I will admit i don't know the exact math, I.E. the spawn timer for minions, the amount of gold minions drop as time progresses, etc... But i feel like the Relic shield can pay for it self in something like 8-10 mins, while the spellthief takes approximately 20 mins, and i wouldn't be surprised if the coin takes the same or longer to pay for it self.

relic shield upgrades and gives an extra 100 health, 50% base health regen, the recharge of the passive goes from 60 seconds down to 30, an extra charge of the passive, the passive heals for 10 more and will go off at 240 (as compared to 200 at teir 1)

Spelltheif's edge upgrade gives +5 ability power, +25% base mana regen, and increase the amount of gold received from landing a basic attack or spell from 5 gold per, to 10 gold per.

Ancient coin upgrade gives 25% base health regen, +10 movement speed, 2 gold per 10 seconds, and a bonus 1 gold for every enemy minion that dies near you without you giving the killing blow.

I personally would like to see the spelltheif items get a bit of a power boost in tier 2 and 3. Maybe something as simple as removing the fact that the passive shuts down for 12 seconds if you kill a minion.