The root "comput-" comes from latin "computo" while "calcolatore" comes from the latin "calculo" which is a rough latin synonym of "computo". The form "comput-" transformed in Italian into "cont-" like in "conto" (English count), "contante" (cash) etc.
So perhaps "contatore" (counter) instead of "computer" would make more etymological sense.
It was picked over the word "calculateur" which is the French equivalent of "calculatore" after IBM France shared a letter wondering if "calculateur" was too restrictive and didn't properly express the machine capabilities. To which Jacques Perret answered "why not ordinateur?"
The problem is the interpretation people give to the word. If I say computer, people think of something with keyboard + mouse and a screen, or maybe a laptop (funny enough, they will not think of their phone).
If I say "calcolatore", we envision one of those devices to do math operations, used in school (are those still a thing?)
In Hebrew we have "tachless" that comes from yiddish "tachless", that comes from Hebrew "tachlit" but now tachless and tachlit have different meanings and different grammar roles
If everybody in Italy understands "computer", calling it "calcolatore" is outright against communication (that word in italian is closer to "device to do math operations", which is technically correct, but not what people imagine)