Vāmana-Jayāditya's Kāśikāvṛtti on Pāṇini's Aṣṭādhyāyi (3.4.37: dāśagoghnau sampradāne)
discusses on the śāstriya meaning of goghna as follows-
nipātanasāmarthyādeva goghna ṛtvigādirucyate, na tu cāṇḍālādiḥ / asatyapi ca gohanane tasya yogyatā goghna ityabhidhīyate //
Due to nipātana sāmarthya, atithis such as ṛtvik, etc. and not cāṇḍāla, etc., are called goghna. Even when there is no gohanana (done by either atithi or ātitheya) here, still due to the yogyatā (of atithi) in gohanana, he is called goghna.
Here, Kāśikāvṛtti makes it clear that goghna doesn't refer to karma of gohanana by atithi or ātitheya, but instead refers to the yogyatā of atithi in the karma of gohanana.
In the Nyāsa commentary on Kāśikāvṛtti, Jinendrabuddhi adds -
yadā tarhi tasmai dātuṁ gaurna hanyate tadā tasya goghna ityabhidhānaṁ na prāpnotītyata āha asatyapītyādi/yathā hyapacannapi yogyatayā pācaka ityucyate, tathā'satyapi gohanane goghneti //
The Nyāsa (aka Kāśikāvivaraṇapañjikā) clarifies that even though there doesn't happen any gohanana when the ātitheya presents the cow to the atithi, still the atithi is called goghna, merely highlighting his yogyatā in gohanana. This is why, due to his yogyatā, he would be called a pācaka, even though he does no pacana (of gomāṁsa). The yogyatā of atithi in gohanana is in that (due to his satkāra by ātitheya) he indirectly makes the gau nyūna and apratiṣṭhita compared to himself. As a result, the gau is indirectly apamānita, which is why it's said that her hanana happens, when truly there is no literal hiṁsā imposed on the gau.
The term goghna is derived from the √han dhātu, and it doesn't have only hiṁsā as its artha. Pāṇini's Dhātupāṭha (2.1012) states the following about √han -
hana hiṁsāgatyoḥ /
As per this, √han has both hiṁsā and gati as its meanings. Apparently, the former meaning is popular unlike the latter. Ignorance about the latter meaning leads to incorrect interpretations (popular in Indological circle) of goghna w.r.t śāstra-vihita nṛyajña.
Gau has been declared as aghnyā in śruti and several Vaidika śāstras.
In Nirukta (3.2), Yāska states - gonāmānyuttarāṇi nava
There are nine names of gau in śruti, which is a reference to Nighaṇṭu (2.11) -
aghnyā / ustrā / ustriyā / ahī / mahī / aditiḥ / iḷā / jagatī / śakvarī / iti nava gonāmāni /
Many bhāṣyakāras including Durgācārya, Devarāja Yajva, etc. follow Yāska's explanation of aghnyā (by citing it and further extrapolating on it) -
aghnyā ahantavyā bhavati / aghaghnīti vā // ~ Nirukta (11.43)
In Śānti Parva (262.47) of Mahābhārata, it's said -
aghnyā iti gavāṁ nāma ka etā hantumarhati /
mahaccakārākuśalaṁ vṛṣaṁ gāṁ vā''labhet tu yaḥ //
Aghnyā is the name of gau, so who can do their hanana?
One who inflicts hiṁsā on vṛṣa or gau, commits a mahāpāpa.
In his commentary Bhāratabhāvadīpa, Nīlakaṇṭha comments on aghnyā-
śrutiprasiddhamaghnyā iti gavāṁ nāma na hantu śakyā aghnyā iti yogāt gavāmavadhyatvaṁ śrautamityarthaḥ /
Since, gau itself is aghnyā, how can its hanana really be a vidhi as per Vedādi śāstras (including primarily śruti, smṛtis, and itihāsa-purāṇas) in nṛyajña? It makes no sense at all to hold such an erroneous pakṣa of taking the use of the term goghna in nṛyajña, as referring to literal gohanana (where hiṁsā is exacted on the aghnyā). Hanana of gau is niṣiddha as per śāstras, not vihita by them, unlike what Indologists propose. So, all interpretations of vidhivākyas should align with this stance, otherwise the interpretation would neither be śāstriya nor āstika.
In his commentary Mitākṣarā on Yājñavalkya smṛti (1.109), Vijñāneśvara states -
mahāntamukṣāṇaṁ dhaureyaṁ mahājaṁ vā śrotriyāyoktalakṣaṇāyopakalpayet "bhavadarbhamayamasmābhiḥ" iti / tatprītyartha, natu dānāya vyāpadanāya vā yayā sarvametadbhavadīyamiti, pratiśrotriyamukṣāsambhavāt, .... tasmātsatkriyādyeva kartavyam / satkriyā svāgatavacanāsanapādyārdhyācamanādidānam /..
A mahā ukṣa (vṛṣabha) or mahā aja (goat) should be presented (upakalpayet) to the śrotriya atithi by saying, "this is presented by us for you" for the sake of your prīti, but not for dāna or vyāpādana as 'this is all yours' (which is simply meant for ātithya, doesn't literally mean that everything of ātitheya belongs to atithi). Clearly, no ukṣa (or aja) is to be given in dāna or its hiṁsā done, otherwise it wouldn't be sambhava to bestow ukṣa to every śrotriya atithi who visits the home. ....Therefore, the kartavya of ātitheya is to do satkāra of the śrotriya by svāgatavacana, āsana, pādya, ardhya, ācamana, etc.
Thus, it should be clear now, that there has never been a sadācāra of gohatyā and bhakṣaṇa of gomāṁsa in nṛyajña (atithipūjanam), as per śāstras. Any contrary views are purely a result of a nāstika & asāstrīya interpretations, and hence should be dismissed by all Vaidikas.