Is it correct to say that 'one who craves for ...' and imply existence of self?

According to SN 12.17, Eternalist have the view ‘The one who acts is the one who experiences’ and annihilationist have the view ‘The one who acts is someone other than the one who experiences.

"'The one who acts is the one who experiences [the result of the act]' amounts to the eternalist statement, 'Existing from the very beginning, stress is self-made.' 'The one who acts is someone other than the one who experiences'[2] amounts to the annihilationist statement, 'For one existing harassed by feeling, stress is other-made.' Avoiding these two extremes, the Tathagata teaches the Dhamma via the middle:

The Buddha teaches via the middle. So our view or the “Buddhist view” would be,

‘From ignorance as a requisite condition come fabrications.
From fabrications as a requisite condition comes consciousness.
From consciousness as a requisite condition comes name-&-form.
From name-&-form as a requisite condition come the six sense media.
From the six sense media as a requisite condition comes contact.
From contact as a requisite condition comes feeling.
From feeling as a requisite condition comes craving.
From craving as a requisite condition comes clinging/sustenance.
From clinging/sustenance as a requisite condition comes becoming.
From becoming as a requisite condition comes birth.
From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of stress & suffering.’

The question or questioner in SN 12.12 obviously was phrased with "self-view", thus perceiving so, the Buddha answered accordingly.

However, in the Saṃyuktāgama, the language is obviously "conventional language".

The Pali is SN 12.12 is "ko nu kho", which when examining the Pali suttas, appears to have no special usage; being used both conventionally (in Udāna 3.9) & as wrong view (in SN 12.12).

“Now who, venerable friends, knows a craft (ko nu kho, āvuso, sippaṃ jānāti)? Who has trained in what craft? Which craft is the greatest of the crafts?”

Then the Gracious One, having understood the significance of it, on that occasion uttered this exalted utterance:

“One who lives without craft, light, desiring others’ welfare, With restrained faculties, completely free in every way, Who wanders homeless, unselfish, not yearning, Having given up conceit, solitary—he is a monk.”

Ud 3.9

There is apparent contradiction, but no real contradiction. The Buddha gave different teachings to different people based upon their skill level and predilection. That is why context is so important to understanding buddhavacana.

Certain teachings are provisional and certain teachings are definitive. If you insist on a dogmatic literal reading of sutta at all times or employ naive historicity in attempting to divine which teachings are provisional and which are definitive you will end up very confused.

So how should we figure out what is provisional and what is definitive? We should use reason, logic, empirical research (ie., putting the teachings into practice and observe the results) and finally try to retrace the accounts of valid teachers.

Now, with this in mind...

Saying “I” does not necessarily imply that identity view arises. When you look in the mirror and say, “there I am” do you for even one moment conceive that you actually are inside that mirror? Do you mistake that mere reflection for even one moment as you? Or are you just using convention? Whenever someone who is no longer fooled - in the same way you would not be fooled by that mirror - by illusion like identity view says “I” it is just like you saying “there I am” to that mere reflection in the mirror.

Our existence is just like that illusion like reflection in the mirror. Most of us don’t know that though and mistake the reflection for something real. Therefore when we say “I” we are actually fooled. To be clear, if isn’t saying “I” that is the mistake. It is being fooled into thinking illusion-like existence is real.

As for craving, think about seeing the reflection of some ice cream in a mirror. Do you for even one moment crave the ice cream in the mirror? Or do you realize that illusion of ice cream is utterly unreal and how could you crave something so unreal? If you saw your own reflection and said “there I am” and then said of that reflection “I have no craving for that ice cream at all” wouldn’t that be true?

It's very simple.

When there is an idea of a delight and craving for that delight - there's goal-making, when there's goal-making - there is acting towards a goal, when there is acting towards a goal - there's receiving of a result of that action, when there's goal-making, acting, and receiving result - there emerges an idea of Agent or Self that sets that goal, acts, and receives the result. This idea of Self keeps accumulating attitudes, tendencies, desires, opinions, motives, motivated actions, and appropriating results of those actions as further opinions and motives - thereby perpetuating itself.

The idea of Self supports Craving. Craving supports the idea of Self. Both support each other through Action motivated by Craving and through thinking about that Action in terms of Self.

As long as there's thinking in terms of Self, there's Craving. As long as there's Craving there's thinking in terms of Self. As long as there are both, there's Suffering.

Which is why Buddha said: One (=Idea of Self) who craves for delight, implicitly craves for dukkha. One who craves for dukkha will act to get more dukkha (by supporting idea of Self), instead of acting to attain liberation from dukkha.

So Buddha was very precise in his use of language. If there's "one who craves" - there's support for maintaining the cycle, there's more craving. And if there's craving, there's support for maintaining the cycle - there's "one who craves".

If someone understands conceptually that his own Self is an illusion, that's already a first step to liberation. But as long as there's still Craving, Attitudes, Opinions, Positions, Views - there's going to be more fuel for Self to seem to exist.

So the next step, is to abandon all Craving - and not just that but also Attachments, Attitudes, Opinions, Positions, Identification, Labels - and anything else that supports the Idea of Self.

Of course when Buddha speaks about the Problem he speaks inside the (Samsaric) framework that has Self. Because the problem only exists inside that framework. Outside of that framework, there is no problem.

When Buddha speaks about the Solution, he speaks inside a framework that does not have self. Because he wants to show an alternative.

When Buddha speaks about Result, he speaks about having no single position and about analysis of dharmas being the ultimate right view. Because both positions - Samsaric as well as the position of No-Self are just one-sided representations of Reality which is the Ultimate Truth.

The Buddha indeed spoke of people or individuals, for example, in AN 4.98:

“Mendicants, these four people are found in the world.
“Cattārome, bhikkhave, puggalā santo saṃvijjamānā lokasmiṃ.

Puggala means individual or person.

Your question is different from this other question. The other question asks about the Buddha saying "I am the unexcelled teacher" - would that be considered as having identity view or conceit.

Your question is about the Buddha referring to a person or individual or self.

Does a self not exist at all? That's not what the Buddha says.

In the Attakari Sutta (AN 6.38), he says:

“So, brahmin, when there is the element of endeavoring, endeavoring beings are clearly discerned; of such beings, this is the self-doer, this, the other-doer. I have not, brahmin, seen or heard such a doctrine, such a view as yours. How, indeed, could one — moving forward by himself, moving back by himself — say ‘There is no self-doer, there is no other-doer’?”

So, there are individuals. There is such a thing as a self.

On the other hand, the Buddha also says in SN 12.12:

“Venerable sir, who craves?”

“Not a valid question,” the Blessed One replied. “I do not say, ‘One craves.’ If I should say, ‘One craves,’ in that case this would be a valid question: ‘Venerable sir, who craves?’ But I do not speak thus. Since I do not speak thus, if one should ask me, ‘Venerable sir, with what as condition does craving come to be?’ this would be a valid question. To this the valid answer is: ‘With feeling as condition, craving comes to be; with craving as condition, clinging; with clinging as condition, existence…. Such is the origin of this whole mass of suffering.’

So, how can we understand this? The Buddha says on the one hand that there is a self-doer, that is an endeavoring being, who moves himself forth and back at will. But on the other hand, when it comes to explaining dependent origination, the Buddha prefers not to speak of a self, but rather speak of the 12 links of dependent origination. There is no suffering person, but there is simply suffering.

The Acela Sutta (SN 12.17) says (paraphrased here):

Again, when the Buddha was asked by the naked ascetic Kassapa whether suffering was of one's own making or of another's or both or neither, the Buddha replied "Do not put it like that." When asked whether there was no suffering or whether the Buddha neither knew nor saw it, the Buddha replied that there was, and that he both knew and saw it. He then said "Kassapa, if one asserts that 'He who makes (it) feels (it): being one existent from the beginning, his suffering is of his own making,' then one arrives at eternalism. But if one asserts that one makes (it), another feels (it); being one existent crushed out by feeling, his suffering is of another's making,' then one arrives at annihilationism. Instead of resorting to either extreme a Tathaagata teaches the Dhamma by the middle way (by dependent origination)"

So, this is an important principle in Buddhism. If you say there is no self, no being at all, then that is annihilationism. If you say there is an eternal being at the core of every person, that is eternalism. Both are to be avoided.

The self is existent. However, it is not permanent or eternal or standalone. This is explained using the vina or lute analogy in the Vina Sutta (SN 35.205).

"Suppose there were a king or king's minister who had never heard the sound of a lute before. He might hear the sound of a lute and say, 'What, my good men, is that sound — so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling?' They would say, 'That, sire, is called a lute, whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' Then he would say, 'Go & fetch me that lute.' They would fetch the lute and say, 'Here, sire, is the lute whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' He would say, 'Enough of your lute. Fetch me just the sound.' Then they would say, 'This lute, sire, is made of numerous components, a great many components. It's through the activity of numerous components that it sounds: that is, in dependence on the body, the skin, the neck, the frame, the strings, the bridge, and the appropriate human effort. Thus it is that this lute — made of numerous components, a great many components — sounds through the activity of numerous components.'

"Then the king would split the lute into ten pieces, a hundred pieces. Having split the lute into ten pieces, a hundred pieces, he would shave it to splinters. Having shaved it to splinters, he would burn it in a fire. Having burned it in a fire, he would reduce it to ashes. Having reduced it to ashes, he would winnow it before a high wind or let it be washed away by a swift-flowing stream. He would then say, 'A sorry thing, this lute — whatever a lute may be — by which people have been so thoroughly tricked & deceived.'

"In the same way, a monk investigates form, however far form may go. He investigates feeling... perception... fabrications... consciousness, however far consciousness may go. As he is investigating form... feeling... perception... fabrications... consciousness, however far consciousness may go, any thoughts of 'me' or 'mine' or 'I am' do not occur to him."

Just as music arises from the inter-working of the different parts of a vina or lute, similarly, the self is like a piece of entertaining music which arises when the orchestra of the five aggregates are playing.

The only way self is related to suffering is according to Yamaka Sutta (SN 22.85):

"In the same way, an uninstructed, run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in their Dhamma; who has no regard for men of integrity, is not well-versed or disciplined in their Dhamma — assumes form (the body) to be the self, or the self as possessing form, or form as in the self, or the self as in form. (and the same applies to the other aggregates)

So, when we read the suttas, we need to understand the context of it. Is the Buddha speaking of beings who do exist in a conventional sense? Or is he digging into the nature of suffering and speaking of dependent origination?