Would a stream enterer no longer need the "I am the owner and heir of my karma" reflection?

Suppose an ordinary being thought the following:

“My friend purchased a new car the other day. That car is useful for them to get from point A to point B. That car is theirs. That car would also be useful for me to get from point A to point B. However, I should not take that car as it is theirs and not mine."

Now, after this ordinary person wins stream entry would they automatically abandon the above thought or perhaps not need it anymore? Isn't this question similar to the OP? I think the answer is clear: the person winning stream entry would still have these discursive thoughts and if they abandoned the conclusion - thinking that it is now permissible or skillful to take the car - they'd be doubly wrong. If they thought that because 'I' and 'mine' were self-views that they no longer believe in or that they have outgrown these childish notions and that it was no longer skillful to refrain from taking the car, they'd be doubly wrong. If someone thought they'd won stream entry while holding the above notions they'd be dangerously wrong.

"Therefore, would a stream enterer also automatically abandon the following skillful reflection or perhaps not need it anymore?"

An Arya being is no longer fooled that the self is truly existing, however an Arya being does not come to the false conclusion that this knowledge refutes the conventional existence of the self. Therefore, emphatically no, an Arya being does not give up skillful means that are based on conventional truths. An Arya being is not held sway to the illusion that this reflection (a conventional truth) has true or ultimate existence. That is the point.

The Buddha did not argue with the world. The Buddha did not reject conventional truth. Upon perceiving the ultimate truth he did not use this to refute the conventional. Doing so would be an error of falling to the extreme of annihilationism.

When you analyze dhammas with reasoning trying to find a self and come up with nothing... to come away from this thinking that the dhammas do not have conventional existence is an error. It would be like analyzing a chariot and trying to find the true existence of the chariot ... is it in the parts? is it in the whole? is it both? neither? and when you come up with nothing ... would you conclude that chariots just don't exist at all? That they have no use in this world since they don't truly exist and you've "outgrown" them??

This question is like asking if an Arya being, after discovering that chariots do not ultimately exist, would use this to deny the conventional existence of chariots and therefore refuse to ever get in one again - preferring to walk instead!

It might be good for people having doubts about this to meditate on this question and read Nagarjuna's 24th chapter of the MMK where he specifically discusses what the doctrine of emptiness implies for the Four Noble Truths - and maybe more importantly - what it emphatically doesn't.

The real danger with this whole line of reasoning - mistaking the result of analyzing for the ultimate as refuting conventional truth - is that nothing whatsoever can withstand ultimate analysis. That is, if you ask whether anything at all has true existence - a pot, a headache, a chariot, a car, persons, evolution, special relativity, quantum mechanics, basic arithmetic, electricity - nothing at all can withstand this analysis. You'll come up empty each and every time. So if you then conclude that pots, headaches, chariots, cars, persons, evolution, special relativity, quantum mechanics, basic arithmetic, electricity are all conventionally non-existent or conventionally false ... boy will you have a hard time living in this world and communicating with your fellow sentient beings. It is just an error. I'd say go back and look again :)

There are several koans in the zen tradition that address this very issue most notably Hyakujo's Fox from the Mumonkan. When one gets a taste - or even a veritable feast - of awakening, the experience can be so profound and liberating that one can think that there is no work left to be done. From the Mahayana perspective, of course, this is patently absurd. Dharma gates are without measure. Our personal karma is taller than Mount Sumeru. Irrespective of how liberating a kensho experience may feel, there's always more work to be done. Seeing a truth is not the same as having worked through it. There is, as another koan puts it, just a little bit of tail that hasn't passed through the window.

No matter how deeply we see into emptiness, we remain in the world of form. A fully enlightened monk may still fall into a well. A roshi may still develop alcohol dependency and I need hardly mention the number of sexual misconduct scandals that have wracked the sangha in recent years. Many of these people were deeply awake, but could not escape their karma. We all fall into causation...at least until we are enlightened without remainder and even then, I wonder.

We may hook the golden carp with the moon, but our foxes wait on the bank with hunger in their eyes. We can never stop reflecting.

I will post this answer just to add on to others' answers. And I will not accept my own answer.

Adding to Andrei's answer, a stream enterer, once-returner and never-returner all would still have conceit or self-habit (a higher fetter), even if they have overcome self-view (a lower fetter). Hence, they may still need this reflection as skillful means.

This is explained in SN 22.89:

"In the same way, friends, even though a noble disciple has abandoned the five lower fetters, he still has with regard to the five clinging-aggregates a lingering residual 'I am' conceit, an 'I am' desire, an 'I am' obsession. But at a later time he keeps focusing on the phenomena of arising & passing away with regard to the five clinging-aggregates: 'Such is form, such its origin, such its disappearance. Such is feeling... Such is perception... Such are fabrications... Such is consciousness, such its origin, such its disappearance.' As he keeps focusing on the arising & passing away of these five clinging-aggregates, the lingering residual 'I am' conceit, 'I am' desire, 'I am' obsession is fully obliterated."

Adding to Buddhism's answer, those who may still be heedless would need this reflection to make hiri and otappa (fear and shame of wrongdoing) the inclination of their awareness.

This is explained in MN 19:

Whatever a monk keeps pursuing with his thinking & pondering, that becomes the inclination of his awareness. If a monk keeps pursuing thinking imbued with sensuality, abandoning thinking imbued with renunciation, his mind is bent by that thinking imbued with sensuality. If a monk keeps pursuing thinking imbued with ill will, abandoning thinking imbued with non-ill will, his mind is bent by that thinking imbued with ill will. If a monk keeps pursuing thinking imbued with harmfulness, abandoning thinking imbued with harmlessness, his mind is bent by that thinking imbued with harmfulness.

I think these excerpt taken from Ajahn Chah Teaching could be the answer:

A sotapanna is still sekha puggala (a person who needs to train) so some of the conventions of teachings are needed.

Usually when we talk about practice we talk about entering and leaving, increasing the positive and removing the negative. But the final result is that all of these are done with.There is the sekha puggala, the person who needs to train in these things, and there is the asekha puggala, the person who no longer needs to train in anything. This is talking about the mind: when the mind has reached this level of full realization, there is nothing more to practice. Why is this? It is because such a person doesn’t have to make use of any of the conventions of teaching and practice. It’s spoken of as someone who has gotten rid of the defilements.

The sekha person has to train in the steps of the path, from the very beginning to the highest level. When they have completed this they are called asekha, meaning they no longer need to train because everything is finished. The things to be trained in are finished. Doubts are finished. There are no qualities to be developed. There are no defilements to remove. Such people dwell in peace. Whatever good or evil there is will not affect them; they are unshakeable no matter what they meet. It is talking about the empty mind. Now you will really be confused.

You don’t understand this at all. “If my mind is empty, how can I walk?” Precisely because the mind is empty. “If the mind is empty, how can I eat? Will I have desire to eat if my mind is empty?” There’s not much benefit in talking about emptiness like this when people haven’t trained properly. They won’t be able to understand it.

Those who use such terms have sought ways to give us some feeling that can lead us to understand the truth. For example, these sankhara that we have been accumulating and carrying from the time of our birth until this moment – the Buddha said that in truth they are not ourselves and they do not belong to us. Why did he say such a thing? There’s no other way to formulate the truth. He spoke in this way for people who have discernment, so that they could gain wisdom. But this is something to contemplate carefully.

Some people will hear the words, “Nothing is mine,” and they will get the idea they should throw away all their possessions. With only superficial understanding, people will get into arguments about what this means and how to apply it. “This is not my self,” doesn’t mean you should end your life or throw away your possessions. It means you should give up attachment. There is the level of conventional reality and the level of ultimate reality – supposition and liberation. On the level of convention, there is Mr. A, Mrs. B, Mr. M., Mrs. N. and so on. We use these suppositions for convenience in communicating and functioning in the world. The Buddha did not teach that we shouldn’t use these things, but that we shouldn’t be attached to them. We should realize that they are empty.

Excerpt from "Toward the unconditioned"

If you think “I’m good,” “I’m bad,” “I’m great,” “I’m the best,” then you are thinking wrongly. If you see all these thoughts as merely determinations and conditions, then when others say “good” or “bad” you can leave it be with them. As long as you still see it as “me” and “you” it’s like having three hornets nests – as soon as you say something the hornets come buzzing out to sting you. The three hornets nests are Self-view, doubt, and attachment to rites and practices.

Once you look into the true nature of determinations and conditions, pride cannot prevail. Other people’s fathers are just like our father, their mothers are just like ours, their children are just like ours. We see the happiness and suffering of other beings as just like ours.

If we see in this way we can come face to face with the future Buddha, it’s not so difficult. Everyone is in the same boat. Then the world will be as smooth as a drumskin. If you want to wait around to meet Phra Sri Ariya Metteyya, the future Buddha, then just don’t practice... you’ll probably be around long enough to see him. But He’s not crazy that he’d take people like that for disciples! Most people just doubt. If you no longer doubt about the self, then no matter what people may say about you, you aren’t concerned, because your mind has let go, it is at peace. Conditions become subdued. Grasping after the forms of practice... that teacher is bad, that place is no good, this is right, that’s wrong... No. There’s none of these things. All this kind of thinking is all smoothed over. You come face to face with the future Buddha. Those who only hold up their hands and pray will never get there.

Excerpt from "Knowing the world"

You can look into this: self-view, skeptical doubt, superstitious at tachment to rites and rituals. The first step is to get free of these. Whatever sort of knowledge you gain, these are the things the mind needs to get free of. What are they like now? To what extent do we still have them? We are the only ones who can know this; we have to know for ourselves. Who else can know better than we? Self-view, doubt, superstition: if we are stuck in attachment here, have doubt here, are still groping here, then there is the conception of self here. But now we can only think, if there is no self, then who is it that takes interest and practises?

All these things go together. If we come to know them through practice and make an end of them, then we live in an ordinary way. Just like the Buddha and the ariyas. They lived just like worldly beings (puthujjana ). They used the same language as worldly beings. Their everyday existence wasn’t really different. They used many of the same conventions. Where they differed was that they didn’t create suffering for themselves with their minds. They had no suffering. This is the crucial point, going beyond suffering, extinguishing suffering. Nibb ¯ana means “extinguishing.” Extinguishing suffering, extinguishing heat and torment, extinguishing doubt and anxiety.

There’s no need to be in doubt about the practice. Whenever there is doubt about something, don’t have doubt about the doubt – look directly at it and crush it like that.

The point of contemplating kamma inheritance is for it to become the inclination of the mind as a dominant perception due to a frequent giving of attention.

A sotapanna can be excessively heedless and has to often reflect on being the heir of the good & bad for the undoing of ill.