Left. 
I wouldn’t say that it follows from it. It is intrinsic to it, it goes both ways. Assuming an inherent existence in the aggregates creates a sense of ‘I’, but assuming an ‘I’ also creates a sense of inherent existence in the aggregates. I think both are important, while it feels to me you’re considering the former alone. And I actually think that fundamentally it is the latter that creates wrong views. E.g. views of eternalism/annihilation really stem from a sense of ‘I’, not from a metaphysical philosophy of an inherent existence.
I’ll explain why I think these things, but first a little correction. It’s not about whether things are “worth” taking as me and so forth, but whether they really are. I take kallaṃ here to mean “fit” as in “proper”, i.e. correct. But either way, it’s only the negative statement that’s worded with kallaṃ; the positive statement isn’t. I assume you won’t have objections to this, but for clarity, let me quote:
“Is what is impermanent, suffering, and subject to change fit to be regarded thus: ‘This is mine, this I am, this is my self’?” - "No, venerable sir.” […]
“Therefore, bhikkhus, any kind of form whatsoever, whether past, future, or present, internal or external, gross or subtle, inferior or superior, far or near, all form should be seen as it really is with correct wisdom thus: ‘This is not mine, this I am not, this is not my self.’ (SN22.59)
This correct understanding already indicates that the concept of self is inherently bound to ‘mine’ and ‘I’, so that ‘personal identity’ is not a bad way to describe what it is about. That’s what I’ll try to argue here. For now, note it says: “not my self”.
So hear me out… 
At some point I translated attā as ‘essence’ because I had similar views as you, Venerable (or what it seems you have). But I realized the concept is bigger than that.
First, I think you argued from anicca to anattā in an earlier post. Basically you said, something being impermanent means it has no inherent existence. Sure. We can of course contemplate that way, from anicca straight to anatta in that sense. Plenty of sutta support for it, and I do it too.
But the Buddha is also saying: “What is suffering, is without self.” (yaṃ dukkhaṃ tadanattā, e.g. SN22.15) We can smuggle in anicca here again by saying, “Well, suffering means impermanence.” But that’s not necessarily true. There is also the suffering of pain itself (dukkhadukkhatā), and the suffering of fabrications (sankhatadukkhatā).
Now, if the concept of attā was purely about a metaphysical essence, then we can’t conclude from pain itself that there is no atta. Why? Because the essence could be inherently painful. Pain would just be it’s inherent nature. People in DN1 claimed such an attā.
So we can’t arrive at anattā from dukkha directly, if we take atta to just be an inherent existing thing. There must be more to this attā.
Here the Anattalakkhana Sutta has something more to say. To not get overly focused on “form”, let’s pick as the aggregate consciousness instead. I’ll use my translation:
Consciousness is without a self. If consciousness were one’s self, you could control it, thinking, ‘My consciousness won’t be like this; it will be like that!’ and it would not result in affliction. But because consciousness is without a self, you can’t control it, and it results in affliction. (SN22.59)
Here the Buddha is actually telling us how we can conclude from dukkha that consciousness is not a self. A self has the quality to control itself. It could make itself this way and that. So there is an assumption of agency in, an assumption of an I that can do something to change something.
The Buddha’s argument is: If we could change things, we would make them happy. But things aren’t happy. Therefore, an agency or I that can change things doesn’t exist. That’s how from dukkha we get to anatta.
So therefore, in the Pāli canon attā doesn’t just have the idea of ‘essence’. It’s a much wider concept.
That’s one indication for what I’m saying. But more so, if we think of atta purely in terms of “inherent essence”, the whole passage falls apart:
Consciousness is without an inherent essence (attā). If consciousness were an inherent essence, you could control it, thinking, ‘My consciousness won’t be like this; it will be like that!’ and it would not result in affliction. But because consciousness is without an inherent essence, you can’t control it, and it results in affliction.
While the Buddha doesn’t directly state here that consciousness does change, clearly it is implied that it can change, just in ways that are beyond control. But now, here’s the point: An inherent existence can’t change! That’s exactly what it means to inherently exist: that it remains the same. So attā cannot mean inherent existence here.
The Buddha meant something else. There’s more to the attā than just ‘essence’. Or, there can be more to it, at least, depending on context. It’s more close to a traditional understanding of soul or, indeed, a self; something we expect to have control over (but don’t because it doesn’t exist).
Of course that also makes complete sense if we consider how the word attā is used in non-philosophical contexts: exactly to refer to the person’s conventional self. As far as I know, it never refers to some inherent essence of something physical or such, but please correct me if so. Usually, that would be words like sāra instead. Which the Buddha occasionally also used to explain anatta (SN22.95), but that doesn’t make atta exactly equal to sāra. That’d be saying apples are fruits so all fruits are apples.
Also, in MN22 views of self are said to arise because of taking things as an I, not from taking something (like a cup) to have an inherent essence. Since all views of self are the result of view of assuming an I (or assuming you are a being), they are intrinsically psychological:
This is how you focus improperly: ‘In the past, did I exist? Did I not exist? What was I? In what way was I? What was I after I was what? In the future, will I exist? Will I not exist? What will I be? In what way will I be? What will I be after I am what?’ Or you are perplexed about the present, thinking: ‘Do I exist? Do I not exist? What am I? In what way am I? Where has this being come from? Where will it go?’ [I.e. annihilation is the belief that the being who you think you are won’t go anywhere.]
If you focus improperly like that, one of six views will arise and seem actual and real: ‘I have a self,’ or ‘I don’t have a self,’ or ‘I perceive a self with a self,’ or ‘I perceive what is not a self with a self,’ or ‘I perceive a self with what is not a self,’ or ‘this self of mine is the one who speaks and feels, who in various realms experiences the results of good and bad deeds; it is permanent, constant, eternal, unchanging, existing for all eternity.’
Even in the Kaccānagotta Sutta, the wrong view of self is not just worded as attā but attā me, ‘my self’. It’s all personal again, about who we take ourselves to be. So even here, even if attā were to only mean ‘essence’ in a general sense, it’s still only about what we take to be our essence. External cups have nothing to do with the wrong view even then, as long as we don’t take them to be our attā. Same in the Anattalakkhana Sutta and many other places.
There’s more passages that point at all this, but in sum: that’s why I stopped translating attā as ‘essence’.
And this is also why earlier I brought up the physicalist/materialist who believes in quantum physics, asking you how they would be annihilationists. Let’s say she believes the body is a collection of quantum possibility wave functions that only mathematically exist. And the mind is just an epiphenomenon of those wave functions. This wouldn’t even be an extreme view amongst scientists nowadays.
Now, I think you’ll have a hard time explaining why such a person would be an annihilationist, if it was all about perceiving some inherent existence in matter and the body, like how you explained a more naturalist materialist earlier.
I would instead just replay: Well, she may hold that physicalist view in theory, but psychologically she still has a sense of self. The concept of self is inherently bound up with ‘me’ and ‘mine’. Since she is not a noble one, psychologically, she simply can’t just believe that the body will cease at death (or that it is just quantum waves no longer collapsing or whatever). She feels she will cease as well. Hence it’s annihilation. Because of that sense of identity.
So when we come down to it, it doesn’t really have much to do with how people like her relate to matter. It’s all about what they believe will happen to “themselves” after death. It is the exact same for annihilationists in the suttas, I’d say. And it’s the same with natthitā, which in my view isn’t some abstract philosophy about inherent essences being annihilated but a feeling of “I won’t exist”. Hence my ‘nonsurvival’, which I plan to support further later.
Come to think of it: A single-life-belief materialist who holds their body is just matter, that matter is just a form of energy, and energy can’t be destroyed, in your view would have to be an eternalist. Why wouldn’t they? After all, they see some permanent essence in rūpa.
Be that as it may, I hope you now understand why I think such approaches are missing a big part of what I think matters to Buddha-dhamma from a psychological perspective. It doesn’t ask questions like, where does this sense of I come from? If we reduce anattā to such contemplations as “form has no inherent existence” we’re likely to leave much of this important psychology out. (This contemplation is also already sufficiently captured by that of impermanence, by the way. To say “form is impermanent” is exactly equal to say “form has no inherent essence”. But anattā is wider than that. To say “form is anatta” also means “form is not me, not mine”.)
Lastly, if anatta was only about an inherent essence, it would already be fully understood by stream winners. To say “consciousness is not an inherent essence” would have no more pragmatic value for them. But the contemplation of anatta is still useful for trainees; the suttas make that quite clear. The point is, for them it’s more so about removing the subtle tendencies of “I” that still linger. Not about some view of essence within one’s being. (Which is arguably the sakkaya ditthi, which the stream enterer already abandoned. Though the term is ambiguous to me.)
This is also why “not I” is in a sense deeper than “no inherent essence”. It get to a more fundamental problem.
I’ll probably leave it at that.
Thanks for the exchange. You’ve nuanced my take on Nāgārjuna a bit. But I still don’t think it’s exactly getting down to the core of what the Buddha was on about. And I’m still sure that this is not what the Kaccanagotta sutta was about.
It’s a straw-man to suppose that Madhyamaka is proposing a new form of metaphysical speculation. It’s not what the system does. It is supposed to give the tools to deconstruct particular ontological views, which are one of the floods (ogha), outflows (āsava) and underlying tendencies (anusaya), and which the Buddha himself refuted. Deconstructing or refuting wrong views is not the same as proposing an opposite view. Refuting eternalism is not the same as arguing for annihilationism.
Bit disappointing. I still think it was a good joke, though. 
, so it will not liked by many.
And sorry at Ven Vaddha for not getting his point.