Is it true that arahants don't have sati?

I have no references to texts, only personal experience. I hope I can still shed some light on your question though. Only so much can be learned through teachings. We must look to personal experience to answer these types of questions. You will never know the true answer until you experience enlightenment for yourself.

I am an arahant, if I can say that. There is no perminant, separate self to be an arahant. But enlightenment occurred, and the paradigm shift occurred.

Sati is translated many ways.

If you translate it as "Mindfulness", you are talking about keeping the teachings in mind to guide your mind towards enlightenment. Once you have awoken completely, there is no need for guidance.

I think what you may be hung up on is the concept of effort. I believed I was working hard to do the "right" thing. I thought I was making choices, and pushing myself where I wanted to go.

It was just belief though. When enlightenment occurs, you see there is no such thing as effort. It stems from a belief that the permanent, separate self makes choices and acts. We do not have free will. We do not choose and we do not act.

What is choice? Choice is a thought. Take the question, "Would you like soup or salad?". You might repeat the question as a thought in your mind. Then there is a pause. Then the thought "I would like salad" comes and goes. Then a thought occurs, "I made a choice".

There was nothing between the question and answer. Did you choose the answer to the question, or did it just appear? Perhaps you have a preference? Did you choose to prefer salad over soup? With the thought "I made a choice", the belief in choosing is created. A choice always appears after it has been made in the form of a present thought.

Why do we believe we have free will? It stems from an innate understanding of what we truly are. We are the universe, creating all minds and experiences. The freedom is in the infinite possibilities of what we can experience. We have no control over our experiences. I don't choose the colors of the trees or the sounds of traffic. All experience is uncontrollable and ever changing. How could effort exist without control?

I do not have sati. There is no I to possess sati. Nothing becomes. All things are.

In my understanding, The Five Powers develop in progression:

• Faith/Conviction (saddhā bala)
• Energy/Effort/Persistence (viriya bala)
• Mindfulness (sati bala)
• Concentration (samādhi bala)
• Wisdom/Discernment (paññā bala)

Each Power supercedes the previous, subsumes it and makes it obsolete.

First, the only Power helping the neophyte move forward on the Path is Faith in Buddha and Dharma.

Then the student, inspired by Faith, develops the power of Effort or "Working Hard", which, while not necessarily removing Faith, certainly supercedes it as the main factor of moving forward.

As the student applies Effort again and again, failing and trying again to overcome ignorance, desire, aversion, and the habitual pathologic mindstates - the power of Mindfulness (=remembering the Instructions during daily activities) develops and becomes the main engine and guardian of one's practice, superceding both Brute Effort as well as Blind Faith.

When the power of Mindfulness fully matures, it grows into ability to maintain the Dharmic perspective, which is a certain choice of interpretation of what's going on. It's not just remebering the teaching anymore, it's a kind of Focus or Concentration, keeping the mind on reality of Dharma-world. When this power fully matures it makes one a different person living in a very different world and supersedes the power of Mindfulness.

Finally, as the student acquires the wisdom of seeing "how things are", the power of Samadhi, or fabricating and maintaining a certain perspective, gives way to Prajna, also known as The Knowledge of All Modes - which is the power of seeing all realities beyond conceptual limitations and skillfully navigating them.

As you see, according to this model at some point sati is overgrown, subsumed and superceded by samadhi.

That's not what DN 16 appears to say. The Buddha, who is also an Arahant, endured his physical pains mindfully (sati) according to DN 16.

After the Buddha had commenced the rainy season residence, he fell severely ill, struck by dreadful pains, close to death.
Atha kho bhagavato vassūpagatassa kharo ābādho uppajji, bāḷhā vedanā vattanti māraṇantikā.

But he endured with mindfulness and situational awareness, without worrying.
Tā sudaṃ bhagavā sato sampajāno adhivāsesi avihaññamāno.

And also:

But the mendicants who were free of desire endured, mindful and aware, thinking:
Ye pana te bhikkhū vītarāgā, te satā sampajānā adhivāsenti:

“Conditions are impermanent. How could it possibly be otherwise?”
“aniccā saṅkhārā, taṃ kutettha labbhā”ti.

Maybe your friend meant to say that an arahant no longer has to consciously make an effort to develop sati? An arahant has developed all 8 limbs of the Noble Eightfold Path to perfection such that they've become second nature. To him, sati's no longer an effort to be developed. It's become his way of life. It's like a novice martial arts student at first has to constantly practicing many drills to build up his reflex and awareness. Once he's become a martial arts master, it'd be absurd to say he "no longer has reflex and awareness", but reflex and awareness have become second nature to him.

The Blessed One said, "Now, what are the eight thoughts of a great person? This Dhamma is for one who is modest, not for one who is self-aggrandizing. This Dhamma is for one who is content, not for one who is discontent. This Dhamma is for one who is reclusive, not for one who is entangled. This Dhamma is for one whose persistence is aroused, not for one who is lazy. This Dhamma is for one whose mindfulness is established, not for one whose mindfulness is confused. This Dhamma is for one whose mind is centered, not for one whose mind is uncentered. This Dhamma is for one endowed with discernment, not for one whose discernment is weak. This Dhamma is for one who enjoys non-objectification, who delights in non-objectification, not for one who enjoys & delights in objectification. ~~ AN 8.30 ~~