license to kill (kāya): SN 47.9 By default, 'kāya' is the physical body (rūpa kāya) made up of 4 elements, porridge, etc.

 Notice how kāya is used in this sutta, in the two places I have highlighted.

Only then [after doing samadhi] does the Realized One’s body become more comfortable.

The Buddha and arahants, by definition, do not feel mental pain, only physical pain.

So if the Buddha's kāya (physical) body is comfortable, it's not a mental body (nāma-kāya) that became comfortable.

By default, when you see kāya in isolation in a meditation context, such as MN 10, MN 119 as prominent examples, it's talking about a physical body (rūpa kāya), not a mental body (nāma-kāya).

And it's not talking about a physical body that also includes a mental body, as this sutta SN 47.9 makes clear.

SN 47.9 Gilāna: Sick

(translation style SP-FLUENT by frankk‍)

9. Gilānasutta	9. Sick
Evaṃ me sutaṃ—	So I have heard.
ekaṃ samayaṃ bhagavā vesāliyaṃ viharati veḷuvagāmake.	At one time the Buddha was staying near Vesālī, at the little village of Beluva.
Tatra kho bhagavā bhikkhū āmantesi:	There the Buddha addressed the monks:
“etha tumhe, bhikkhave, samantā vesāliyā yathāmittaṃ yathāsandiṭṭhaṃ yathāsambhattaṃ vassaṃ upetha.	“monks, please enter the rainy season residence with whatever friends or acquaintances you have around Vesālī.
Idhevāhaṃ veḷuvagāmake vassaṃ upagacchāmī”ti.	I’ll commence the rainy season residence right here in the little village of Beluva.”
“Evaṃ, bhante”ti kho te bhikkhū bhagavato paṭissutvā samantā vesāliyā yathāmittaṃ yathāsandiṭṭhaṃ yathāsambhattaṃ vassaṃ upagacchuṃ.	“Yes, sir,” those monks replied. They did as the Buddha said,
Bhagavā pana tattheva veḷuvagāmake vassaṃ upagacchi.	while the Buddha commenced the rainy season residence right there in the little village of Beluva.
Atha kho bhagavato vassūpagatassa kharo ābādho uppajji, bāḷhā vedanā vattanti māraṇantikā.	After the Buddha had commenced the rainy season residence, he fell severely ill, struck by dreadful pains, close to death.
Tatra sudaṃ bhagavā sato sampajāno adhivāsesi avihaññamāno.	But he endured with rememberfulness and lucid-discerning, without worrying.
Atha kho bhagavato etadahosi:	Then it occurred to the Buddha:
“na kho me taṃ patirūpaṃ, yohaṃ anāmantetvā upaṭṭhāke anapaloketvā bhikkhusaṃghaṃ parinibbāyeyyaṃ.	“It would not be appropriate for me to become fully nirvana'd before informing my attendants and taking leave of the monk Saṅgha.
Yannūnāhaṃ imaṃ ābādhaṃ vīriyena paṭipaṇāmetvā jīvitasaṅkhāraṃ adhiṭṭhāya vihareyyan”ti.	Why don’t I forcefully suppress this illness, stabilize the life force, and live on?”
Atha kho bhagavā taṃ ābādhaṃ vīriyena paṭipaṇāmetvā jīvitasaṅkhāraṃ adhiṭṭhāya vihāsi.	So that is what he did.
Atha kho bhagavato so ābādho paṭippassambhi.	Then the Buddha’s illness died down.
Atha kho bhagavā gilānā vuṭṭhito aciravuṭṭhito gelaññā vihārā nikkhamitvā vihārapacchāyāyaṃ paññatte āsane nisīdi.	Soon after the Buddha had recovered from that sickness, he came out from his dwelling and sat in the shade of the porch on the seat spread out.
Atha kho āyasmā ānando yena bhagavā tenupasaṅkami; upasaṅkamitvā bhagavantaṃ abhivādetvā ekamantaṃ nisīdi. Ekamantaṃ nisinno kho āyasmā ānando bhagavantaṃ etadavoca:	Then Venerable Ānanda went up to the Buddha, bowed, sat down to one side, and said to him:
“diṭṭho me, bhante, bhagavato phāsu;	“Sir, it’s fantastic that the Buddha is comfortable,
diṭṭhaṃ, bhante, bhagavato khamanīyaṃ;	that he’s well,
diṭṭhaṃ, bhante, bhagavato yāpanīyaṃ.	and that he’s alright.
Api ca me, bhante, madhurakajāto viya kāyo, disāpi me na pakkhāyanti, dhammāpi maṃ nappaṭibhanti bhagavato gelaññena.	Because when the Buddha was sick, my body felt like it was drugged. I was disorientated, and The Dharmas weren’t clear to me.
Api ca me, bhante, ahosi kācideva assāsamattā:	Still, at least I was consoled by the thought that
‘na tāva bhagavā parinibbāyissati, na yāva bhagavā bhikkhusaṃghaṃ ārabbha kiñcideva udāharatī’”ti.	the Buddha won’t become fully nirvana'd without making some statement regarding the Saṅgha of monks.”
“Kiṃ pana dāni, ānanda, bhikkhusaṃgho mayi paccāsīsati?	“But what could the monk Saṅgha expect from me now, Ānanda?
Desito, ānanda, mayā dhammo anantaraṃ abāhiraṃ karitvā.	I’ve taught the Dhamma without making any distinction between secret and public Dharmas.
Natthānanda, tathāgatassa dhammesu ācariyamuṭṭhi.	The Realized One doesn’t have the closed fist of a teacher when it comes to The Dharmas.
Yassa nūna, ānanda, evamassa:	If there’s anyone who thinks:
‘ahaṃ bhikkhusaṃghaṃ pariharissāmī’ti vā, ‘mamuddesiko bhikkhusaṃgho’ti vā, so nūna, ānanda, bhikkhusaṃghaṃ ārabbha kiñcideva udāhareyya.	‘I’ll take charge of the Saṅgha of monks,’ or ‘the Saṅgha of monks is meant for me,’ let them make a statement regarding the Saṅgha.
Tathāgatassa kho, ānanda, na evaṃ hoti:	But the Realized One doesn’t think like this,
‘ahaṃ bhikkhusaṃghaṃ pariharissāmī’ti vā, ‘mamuddesiko bhikkhusaṃgho’ti vā.
Sa kiṃ, ānanda, tathāgato bhikkhusaṃghaṃ ārabbha kiñcideva udāharissati.	so why should he make some statement regarding the Saṅgha?
Etarahi kho panāhaṃ, ānanda, jiṇṇo vuddho mahallako addhagato vayoanuppatto.	I’m now old, elderly and senior. I’m advanced in years and have reached the final stage of life.
Āsītiko me vayo vattati.	I’m currently eighty years old.
Seyyathāpi, ānanda, jajjarasakaṭaṃ veḷamissakena yāpeti;	Just as a decrepit cart keeps going by relying on straps,
evameva kho, ānanda, veḷamissakena maññe tathāgatassa kāyo yāpeti.	in the same way, the Realized One’s body keeps going by relying on straps, or so you’d think.
Yasmiṃ, ānanda, samaye tathāgato sabbanimittānaṃ amanasikārā ekaccānaṃ vedanānaṃ nirodhā animittaṃ cetosamādhiṃ upasampajja viharati, phāsutaro, ānanda, tasmiṃ samaye tathāgatassa kāyo hoti.	Sometimes the Realized One, not focusing on any signs, and with the cessation of certain feelings, enters and remains in the signless undistractible-lucidity of the heart. Only then does the Realized One’s body become more comfortable.
Tasmātihānanda, attadīpā viharatha attasaraṇā anaññasaraṇā, dhammadīpā dhammasaraṇā anaññasaraṇā.	So Ānanda, be your own island, your own refuge, with no other refuge. Let The Dharma be your island and your refuge, with no other refuge.
Kathañcānanda, bhikkhu attadīpo viharati attasaraṇo anaññasaraṇo, dhammadīpo dhammasaraṇo anaññasaraṇo?	And how does a monk do this?
Idhānanda, bhikkhu	It’s when …

(standard 4sp🐘 formula)

kāye kāyā-(a)nu-passī viharati	He lives continuously seeing the body as a body [as it truly is].
vedanāsu vedanā-(a)nu-passī viharati	He lives continuously seeing sensations as sensations [as it truly is].
citte cittā-(a)nu-passī viharati	He lives continuously seeing a mind as a mind [as it truly is].
dhammesu dhammā-(a)nu-passī viharati	He lives continuously seeing ☸Dharma as ☸Dharma [as it truly is].
(… elided refrain from each way…)	[in each of the 4 ways of remembering]:
ātāpī sampajāno satimā,	he is ardent 🏹, he has lucid discerning 👁, he remembers 🐘 [to apply relevant ☸Dharma].
vineyya loke abhijjhā-do-manassaṃ;	he should remove greed and distress regarding the world.

Evaṃ kho, ānanda, bhikkhu attadīpo viharati attasaraṇo anaññasaraṇo, dhammadīpo dhammasaraṇo anaññasaraṇo.	That’s how a monk is their own island, their own refuge, with no other refuge. That’s how The Dharma is their island and their refuge, with no other refuge.
Ye hi keci, ānanda, etarahi vā mamaccaye vā attadīpā viharissanti attasaraṇā anaññasaraṇā, dhammadīpā dhammasaraṇā anaññasaraṇā; tamatagge mete, ānanda, bhikkhū bhavissanti ye keci sikkhākāmā”ti.	Whether now or after I have passed, any who shall live as their own island, their own refuge, with no other refuge; with The Dharma as their island and their refuge, with no other refuge—those monks of mine who want to train shall be among the best of the best.”

(end of sutta⏹️)

Conclusion

Yet, you have popular famous monks like Ajahn Brahm and Sujato who gave themselves a license to kill kāya whenever they want in the suttas they translate. They can turn kāya into a physical body or a mental body devoid of a physical body whenever it suits their agenda.

This makes their sutta translations on jhāna incoherent, inconsistent, and unusable.

Even Brahm and Sujato can not teach their students how to do their redefined "jhāna" from the suttas alone. They have to provide a special dictionary where they redefine body to mean "mental body devoid of physical body", thinking as "not thinking", material form of 4 elements as "visual appearance devoid of solidity".

And even then, their students still can't do their redefined "jhāna" based in reading their corrupted sutta translations.

See Sujato's AN 8.63, and SN 47.10 for example. It reads like complete gibberish. There's no way anyone can meditate on the 7 awakening factors and develop jhāna (real Buddha jhāna or their redefined "jhāna") from that translation. 

If I used their translation methodology, giving myself a license to ambiguate and change meanings of important fundamental words like they do, I could translate the Quoran and Christian Bible into an accurate guide to the four noble truths leading to nirvana.

Kāya by default, is the physical body in a meditation and other contexts

Especially check out DN 2 and MN 13

https://lucid24.org/tped/k/kaya/index.html#kaya