I know that Germanica non leguntur in some quarters but anyway,
Fritz and Meier-Brügger 2021 (10th ed.), section G506 (pp. 69-71), btw this is a popular introductory textbook:
"Für equus bedeutet dies, dass vom Lat. aus nicht zu entscheiden ist, ob in diesem Fall -qu- auf *-ku̯ oder *-k̑u̯ zurückgeht. Das Iir. macht in unserem Fall die Entscheidung für *-k̑u̯ aber leicht." [p. 70, emphasis mine - Alex B.]. See p. 70 for their analysis of the relevant Indo-Iranian data.
"Zum -pp-: Die ursprüngliche Doppelkonsonanz -*-ku̯ ist vermutlich bereits vormyk. durch -ku̯ ku̯- ersetzt worden (daraus dann nach Beseitigung der Labiovelare neu ein -pp-, s.u. P 343 Abs. 4).
Hinweise auf ein altes -ku̯ ku̯- geben die bereits myk. Schreibung als i-qo (ein mögliches *i-ko-wo kommt nicht vor) und die im alphabetischen Gr. notierte Doppelkonsonanz."
(cf. p. 55, English translation of the 8th German ed. by Charles Gertmenian, 2003):
also see NIL s.v. *h1ék̑u̯o- and Meillet 1908 Introduction a l'étude comparative des langues indo-européennes (p. 64).
I have not seen any other serious proposal yet but I am very open-minded and I would be happy to consider another analysis backed up by relevant language data (examples!) and linguistic theory. And I also hope we can examine other data re: *ḱw > *kʷ rather than focusing solely on possible ad-hoc explanations of the root vowel or gemination in ἵππος with a heterosyllabic cluster, Wetzels 2002: 312 explains the gemination due to w losing its segmental status, Meier-Brügger 2017 writes it "underwent gemination to maintain the original prosodic structure of the etymon" (p. 701), i.e. *kw > *kʷkʷ > *kwkw > pp etc - proposals galore, for an excellent review see
Bernabé, Alberto. "The Noun for ‘Horse’ in Mycenaean and Some Related Terms". Synchrony and Diachrony of Ancient Greek: Language, Linguistics and Philology, edited by Georgios K. Giannakis, Luz Conti, Jesús de la Villa and Raquel Fornieles, Berlin, Boston: De Gruyter, 2021, pp. 115-124. https://doi.org/10.1515/9783110719192-008
Some important ideas from Bernabé 2021:
- “In Mycenean the spellings for ancient k+w (as in ‘horse’) are
clearly distinguished from the ones for k+w in morpheme boundary”
Cf. i-qo, e-qe-a-o, e-qe-o vs. te-tu-ko-wo-a, o-da-ku-we-ta
- Aspiration in Greek is secondary (p. 120),
Tarentine ἴκκος, Macedonian Ἰκκότας, compounds like λεύκιππος; Mycenian e-pi-qo-i (if aspirated, it would have been †e-pi-i-qo-i), pace Perpillou 2004:175 and Garcia Ramon 2016: 218, 220, 228.
- Melena 2014: 15 (ft. 29) “the labiovelar series can be also used for writing clusters of inherited dorsals plus /w/”, e.g. he reads i-qo as /ikwos/ and not the usual /ikkwos/
Bernabé also argues that
"The use of a sign of the q- series instead of a sequence like †i-ku-wo seems to denote that the phoneme that existed between the two vowels was pronounced in a very similar way to that of the labiovelars, whereas the fact that the “morpheme boundary” spelling was not used can probably be attributed to the fact that the sequence was not perceived in the same way in one case (-kkw-) as it was in the other (-k+w-). But neither would be an absolute coincidence with the results of the original labiovelar, because this cluster resulted in geminated -ππ- in the first millennium, while the labiovelar before o gives π, not a geminated. It therefore seems most likely that what we had in Mycenaean was a geminated labiovelar, /kkw/, so when the sequence with *kwo resulted in πo, the sequence with geminated *-kkwο- resulted in -ππo-. On the "other hand, /-kkw-/ and /-kw-/ are not distinguished in the Mycenaean script, because there is never a graphic distinction between simple and geminated consonants. We found other possible cases of geminated labiovelar in Mycenaean: mo-ro-qa, *μοιρόκκwᾱς, ‘owner of a plot or lot of land’, composed of μοῖρα ‘part’ and the verb πέπᾱμαι (see Boeotian τὰ ππαματα, where ππ- comes from -kw-), and also the anthroponym of the same root pi-ro-qa-wo[, *Φιλοκκwᾱϝων. Likewise, through comparison with the geminated Eol. ὄττι we can postulate a geminated voiceless labiovelar, product of an assimilation *d + kw > *kkw, for the term jo-qi, yόκκwι(δ) < *yod-kwid ‘what’. We still have a voiced correlate in the compound pe-qa-to, which must be reconstructed as *πέγγwατον “floor” (of the chariot) < πεδ- followed by the initial *gw- of the root of βαίνω" (pp. 121-122).
If you want to get a broader view, with an extensive historical review, see Otkupshchikov 1989/2001 (Откупщиков 1989/2001), in Ряды индоевропейских гуттуральных