I’m not so sure it’s as crystal clear as you state…
-trix is a suffix occurring in loanwords from Latin, where it formed feminine nouns or adjectives corresponding to agent nouns ending in -tor (Bellatrix). On this model, -trix is used in English to form feminine nouns (aviatrix; executrix) and geometrical terms denoting straight lines (directrix).
Now the
avia comes from
avian/avis which is Latin for bird which derives from
aetós in Greek. Now seeing aviation is a fairly modern phenomena then the etymology of someone who flies is likely to be pretty modern - so the etymology for "aircraft pilot," 1887, from French aviateur, from Latin avis "bird" + -ateur (the common French suffix for someone who does something - like dominateur where the feminine is dominatrice or more commonly in English dominator and dominatrix). The English feminine form of aviatrix is from 1927; the earlier French aviatrice is from 1910, and an earlier English aviatress was first used in 1911.
Now those terms would have been very fresh as Raymonde de Laroche was the first woman to fly a powered aircraft as a Pilot with a licence on 8th March 1910. So really the etymology and its usage starts around that time, where aviatrice, aviatress and aviatrix are effectively correct in their own respective rights.
Another reference here on the more modern use of
-trix is here:
https://www.affixes.org/alpha/t/-trix.html