You have no idea what you are saying. "Supports don't need gold to be relevant." Lmfao. What are you even smoking.
Although a "budget" support kit on a small group of specific champs is inexpensive, Support is by no means a cheap role nor one that performs adequately with the "budget" kit.
Their income has been reduced 3 ways in the last year: Gold items. Minion Lockouts. Loss of Bounty gold.
Since then, you'll notice support picks are leaning toward those who can:
- Use support trinkets that don't lock out minions.
- Use Supports who can take kills to supplement income.
- are not actually Supports.
But..... about the only "non support" who is actually notorious in the role is
, and that has nothing at all to do with gold budgeting or his actual viability as a "support building support."
It has to do with :
V8.1
Blaze
Damage per stack increased to 4% of target's maximum health from 2%.
He was running 52% when they implemented this buff!
Unlike other mages, he actually doesn't need items, because his passive stacked is carrying him.
But if you try to play
with a Budget build, I will walk ALL OVER YOU.
And then you need to compare the upcoming cost of an adc to
.
/
Costs 13,700
Upcoming adc build:

Costs 14,400.
Now..... adc sells
for 180g, so her cost is really
14,220.
That's 520G different than the Zyra Support.
Yet the adc has the fundamental gold earning method. Zyra has to hope for kills, and constant fights to feed 
And you might try to argue that Zyra has a larger impact than an adc, but that's not actually true Mid -Late game, especially if an adc gets to
or
. The build I mentioned has no options for BOTH Grievous Wounds AND Mag Penetration, so Zyra either has to earn more and sell her support item, or she doesn't get both. Or she has to sacrifice CDR and thus damage. Adc gets it all in a single item, and actually gets True damage. Thus, Zyra falls off while the adc keeps scaling.
On Nami, AP has ALWAYS been more effective than the active item build.