Cherish etymology.

I often complain of how many, or most as it seems (if not all) English etymologists stop their research at either Old High German or Latin, neglecting possible Greek heritance. Here is an example:

cherish (v.)

early 14c., cherischen, from Old French cheriss-, present participle stem of chierir "to hold dear" (12c., Modern French chérir), from chier "dear," from Latin carus "dear, costly, beloved" (see whore). The Latin word also is the source of Italian, Spanish, Portuguese caro; Old Provençal, Catalan car. Related: Cherished; cherishing.
http://www.etymonline.com/index.php?term=cherish

All "English" etymologies I can find stop at Latin carus. I looked up the Italian etymology of "caro" and it seems it comes from Greek chairo (χαίρω)
http://www.etimo.it/?term=caro

In another I found it most probably passed to the Latin Language as carestia from acharistia - ingratitude, "contaminated" in meaning by the Latin caritas (Love).
https://unaparolaalgiorno.it/significato/C/caro