When Marc Antony famously fell on his sword after the Battle of Actium, he chose a voluntary death (mortem voluntariam), not because it sounded more noble, but because he couldn't commit suicidium until some clever Englishman coined the New Latin word sometime in the 1650s.
Suicidium is literally an of oneself killing that follows standard patterns of forming new Latin words in later centuries which, alas, the Ancients had not had the foresight to invent.
Even so, Latin purists of the day strongly objected to the coinage, one critic pointing out that the word might as well mean the killing of a sow (sus, Gen. suis).
The modern equivalent of sow versus self is the notion that combining a Latin prefix and a word of Greek origin or the reverse is the linguistic version of wearing stripes with plaids, as if the ghosts of ancient writers were peering over the shoulders of scientists, inventors, and physicians as they coined new words for phenomena that were unheard of in Late Antiquity.
When horseless carriage began to seem a bit silly, English looked to the recent French coinage of véhicule automobile, the adjective formed from Greek -auto and Latin mobilis and voilá! a self-moving (thing) was born — of mixed parentage to be sure, but it still does the job. While to this day a car in Athens is the purely Greek autokineto, the corresponding Latin would be — what?— suimobile? And that might have started the whole sow and self fracas all over again.
The point is that once Greek and Latin enter modern languages like French and English, they soon become as native as baguettes or bacon and can be, and are, freely conjoined without giving their ancient provenance a second thought.
aquaphobia, polyamorous, homosexual, heterosexual, quadraplegic, biathlon, dysfunction, liposuction, electrocution, bigamy, bioluminescence, hexadecimal, genocide, hyperactive, monolingual, neuroscience
All these so-called hybrid words are legitimate coinages, though they freely mix Greek and Latin derivations. Preventing them from doing so out of some misguided sense of linguistic purity would impoverish rather than enrich the language.