Ancient Greek had many consonant clusters, like /pn/ in pneuma, /bd/ in bdellion, and /pt/ in pteron. But for some reason, /ks/ (ξ) and /ps/ (ψ) received special real estate in the 24-letter Greek alphabet. What was the logic behind this decision? Are there any theories by classicists on why writers of Greek found these two consonant clusters so important that they got dedicated letters?
There are multiple possible reasons.
Synchronically, /ks/ & /ps/ are the only clusters that commonly occur word or syllable-finally and they also frequently occur as a result of inflection. Other clusters typically only occur word or syllable-initially or across syllable boundaries, and either as part of the root or due to derivational affixes.
It's possible this could have motivated their special treatment compared to most other clusters (other than zeta - /zd~dz/).
Diachronically we can look at the origin of the Greek alphabet in Phoenician.
Phoenician had a large inventory of sibilants: s, ṣ, š, and z corresponding to the letters samekh, tzade, shin, and zayin (using the Hebrew names of the letters). The exact phonetics of these is not entirely certain and varied over time and likely by location as well. At the earliest stages these were probably /ts/, /tsˤ~tsʼ/, /s/, and /dz/ respectively.
Meanwhile, by the time of the adoption of the Greek alphabet, the various Greek dialects each generally had just two sibilants: σ or Ϻ (depending on location) /s/ and ζ /zd~dz/ (with the realisation of ζ likely varying by dialect).
Unsurprisingly, there seems to have been significant confusion between the four Phoenician sibilants during the adoption of the alphabet, in particular at least three of the letters have shapes and positions corresponding to a different letter than the one they derive their name from.
Greek /dz~zd/ is represented by zeta, which has the shape and position of zayin /dz/, with its name either adjusted by anticipation of the following letter - eta, or continuing the name of tsade /tsˤ~tsʼ/.
The representation of Greek /s/ varied by location, either:
- Sigma: which takes its shape and position from shin /s/, but derives its name from samekh /ts/
- San: which takes its shape and position from tsade /tsˤ~tsʼ/, but derives its name either from shin /s/ or zayin /dz~zd/
That left a letter shape (and position in the alphabet) left over - that of samekh /ts/.
It has been observed by Jackson Crawford when discussing the Old Italic alphabets (and the origin of the runes) that when adopting an alphabet people tend to retain every letter of the original (and possibly add new letters if needed), but are usually reluctant to discard letters of the original even if they aren't needed to represent the phonology of the adopting language. This either leads to multiple letters representing the same sound, or letters being repurposed for entirely new purposes.
Cf Etruscan's dorsal stops, where they retained all four archaic greek letters for dorsal stops (kappa, gamma, chi, and qoppa ) to represent their two phonemic dorsal stops /k/ and /kʰ/, with the choice of whether to represent a /k/ with kappa, gamma, or qoppa depending on the following vowel (which gave rise to the modern use of <q> almost exclusively in the digraph <qu> for /kw/).
Following that principle, the Greeks put samekh to a new use for another cluster of a stop followed by /s/ - /ks/ and gave it a new acrophonic name xi.
That then left /ps/ as the only cluster of a stop followed by a sibilant (the others being /ks/ and /zd~dz/), and this asymmetry may have motivated them to create a new letter for it.
In practice, it's likely both played a role.