Solution to a typological problem about PIE phonology: are there any facts that contradict this view?

Question

Traditionally, PIE phonology postulates three voiceless velar/uvular stops to PIE:

*/ḱ/ (c), */k/ (q), */kʷ/ (q̆)

But I made a search for a PIE dictionary with come 11-15 thousand words, and found only one occurrence of the combination ku̯, in word kroku̯a̯ "border post" which is highly untypical, while kʷ is abundant.kʷ

Given this fact, the only explanation that comes to mind is the idea that there was actually no kʷ in PIE but rather in most cases it was a combination ku̯. This theory would be refuted if there were many kʷ in the end of the roots: in that case after applying this theory we would have roots ending with -ku̯ which is prohibited. So I searched for -ekʷ- composition throughout the roots so to check if it actually frequent.

And what I found?

In many cases either the u̯ in -eku̯- can be part of a suffix, or the *kʷ can be actually reconstructed as *p!

Some examples:

soq̆os "sap" - may be actually, sopos

teq̆os "running water" - may be actually, tequ̯os (suffix -u̯-)

a̯eq̆ea̯ "water body" - may be actually a̯epea̯ (this root a̯ep- for water is actually reconstructed along a̯eq̆ea̯)

u̯lq̆os "wolf" could be actually u̯lquos (suffix), or u̯lpos or lupos

coq̆r "excrement" could be copr (compare "coprophagy")

i̯eq̆r "liver" could be i̯epr (compare "hepatitis")

o̯oq̆ "eye" could be o̯oqu̯-, a typical u-stem (while -q̆ stem is highly untypical)

peq̆ter "cook" could be pepter (compare "peptide").

If this is wrong, what could be the solution to the problem?

---

A similar solution that the voiced equivalent to q̆, ğ at the end of the roots, could be actually b may explain why PIE has very rare *b. For example, traditionally reconstructed e̯reğos "darkness" could be actually e̯rebos which literally coincides with Greek word for "darkness", "erebos"!

See also this question What evidence supports labialized velars in PIE?

---

Note that the traditional phonology implies that in several unrelated branches such as Hellenic, Osco-Umbrian and Celtic, happened similar change:

kʷ->p

which seems to me highly unlikely. It also postulates

kʷ->p->f in Germanic, but not root-initially!

So that

penkʷe -> finf

u̯lkʷos -> wolf

but

kʷod -> what

kʷor -> where

This supports my idea that root-initially kʷ could be actually ku̯ but root-finally it was p because ku̯ root-finally is impossible due to sonority rule (u̯ being sonorant cannot be further from the root nucleus than stop k)

Answer 1

This proposal creates a lot more problems than it solves. First, I don't think the rarity of the biphonemic sequence /kw/ is that problematic: plain velars are relatively infrequent in any case, so it's not too strange if /kw/ happens not to occur in the subset of the PIE lexicon that has been reconstructed. Especially so given that it would have competed with a similar-sounding single phoneme /kʷ/, which might easily have led to merger, or else possibly to dissimilation into /ḱw/. (There are also of course IE scholars who don't believe in the plain velar series at all and think that there were only two velar series, in which case the problem doesn't arise, but this is a minority position.)

Secondly, changing all the reconstructed /kʷ/ into /kw/ actually creates a massive statistical anomaly, since labiovelars are at least as common as plain velars; so this would mean that PIE has more instances of /k/ followed by /w/ than it had of /k/ followed by all other sounds combined, which is highly improbable.

Third, you'd have to explain why this biphonemic sequence shows up as a single phoneme in most of the daughter languages. For example, in the satem languages, why would /w/ have been lost after a velar but not otherwise? In Greek, why would */ḱw/ yield /pp/ (as in hippos), but */kw/ yield /p/ or /t/ and not /pp/ or /tt/?

Replacing labiovelars with labials leads to other problems: you would have to say that */p/ became /kʷ/ or /kw/ in some branches, to account for e.g. Latin aqua, which is a bizarre and to my knowledge unattested change. This would also have to be parallel innovation in those branches, so it's no better in that sense than the standard */kʷ/ > /p/ change. Moreover, it would have to be irregular, since obviously most instances of PIE */p/ remain labial in all the languages.