"I am agony" is, in my opinion, an interesting idea. I would like to see it explored, though I won't necessarily argue that it will be. I will explain why I find it appealing, though.
Epilogue Recap
In the end of The Man in Room 1280, William Afton is wheeled out to a Fazbear Ent distribution center, where his body explodes. His flesh, blood, and by extension, pieces of his soul, get all over the place, haunting some of the items which feature in other stories. Andrew's spirit, which was latched onto Afton's, is distributed as well. In the stingers, the Stitchwraith (with Jake in control) goes around finding these objects, to put Andrew back together. Inadvertantly, he also bring's Afton's pieces together. Afton finishes the job, sucking his own pieces together to form a huge trash conglomerate, declaring "I am agony." Afton himself is said to be weak, though, relying on Eleanor to maintain himself. When Eleanor leaves, the Puppet appears, does something, and Afton's miscreation falls apart, his pieces sinking into a lake.Soul Shattering and Hyperbolic Suffering
Some people have been disappointed by the idea that Afton likes being Springtrap. In FNaF3, Springtrap is Afton's punishment, it's the prison he's forced into by the children, to make him suffer for what he's done, in the same way the children suffered. His "I always come back" shtick would seem to undermine this, because it means that becoming Springtrap was actually in his best interest.I would argue these two ideas can (and do) coexist. It's true that Springtrap is a prison, causing Afton to suffer for 30+ years. It's also true that he got what he wanted, though maybe not in exactly the way he anticipated. It's more of a silver lining, making the most of a bad situation. Look at the way Springtrap is presented in the novels. At first, he's filled with energy, excitedly declaring "I am Springtrap!" But by the time of The Fourth Closet, he's become exhausted by it, to the point where he's had Baby surgically separate him from the suit. Being Springtrap is, in many ways, exactly what he wanted, but it's also holding him in a state of perpetual pain.
Now, look at UCN. Afton is kept alive by the vengeful spirit, to be tortured indefinitely. Again, in a way, this is in his best interest, since it keeps him alive, eventually allowing him to escape. But that doesn't mean UCN isn't also a horrible, torturous experience for him. The point is that the children keep trying to get back at Afton, to make him suffer, and they're succeeding. Afton is arguably the character who suffers most in the story. But it's also what's keeping him alive. Afton cannot be defeated through vengence. The spirits must let him go, but they can't.
It's been said that FNaF is a story about moving on from the tragedies of the past. I'm inclined to frame this a little differently, though. Moving on is the end goal. More often, FNaF is about failing to move on, and then suffering the consequences.
Possibly the biggest takeaway from Fazbear Frights is the association of paranormal effects with the feeling of agony. This gives us a clear reason why Afton can't be defeated through suffering: Suffering is literally what keeps him alive. Afton's story is a slow escalation of agony, as he continually, deperately hangs onto life through ever increasing pain, because this amount of pain is what it takes to become immortal. Afton's declaration that he is agony is certainly dramatic, but it's clearly not that far off.
Agony is also associated with brokenness, with a spirit being shattered into pieces, which can individually haunt many different objects. We see this happen to him in the Frights, where his haunted objects serve as the focus of several stories. It's why he's described as weak, relying on Eleanor for power, because his soul is entirely broken. This is how Afton can "become Agony", leaking out and infecting the world MemoryVictim-style (or NetworkVictim-style, if you prefer). In taking on this highly distributed form, he may effectively become a sort of undergrowth in physical reality, a mindless force of nature in the background of Fazbear Ent. His mind would be completely shattered, of course, so he'd be an "idiot god". He'd have no more coherent thought, only memory, pain, and perhaps will. It's a natural final destination to his quest for immortality, to transcend ordinary existence entirely, at the cost of all human resemblance, and all association with comprehensible reality.
"No, Giygas is no longer the wielder of evil. He has become the embodiment of evil itself... which he cannot control on his own. [...] Giygas cannot think rationonally any more, and he isn't even aware of what he is doing now. His own mind was destroyed by his incredible power. What an all-mighty idiot!"
It's a natural conclusion of his arrogant desperation for immortality, to collapse under his own weight, overpowered by his own painful existence, becoming immortal, but effectively destroying himself in the process. He refuses to go to Hell, but Hell comes to him all the same.
This really isn't that crazy of an idea, considering how similar it is to BV's situation. This is all, more or less, a precedented thing that can happen in the FNaF universe. It's been established, foreshadowed even.
Is this actually a plausible theory? I have no idea. My fondness for cosmic horror may be tinting my judgement. It's possible that it's compatible with the current story, but unintentional, perhaps unfalsifiable. I think it's a fun concept, though, and you (you specifically) should write lots of fanfiction about it, and then send it to me.