Not disagreeing with you either, but as an Italian it's not the C, it's the combination of C and other letters after it.
Cane (dog) and cena (dinner) in Italian are two examples of soft and hard C that depend on which vowel follows the letter C.
It wasn't like that originally, Roman C sounded always like K, Caesar was pronounced Kaesar (German's Kaiser comes from it).
Than middle age came and things changed, but the pronunciation stayed consistent after that
C+a, C+o, C+u = hard C
C+e, C+i = soft C
So it's not simply about "what you write is what you get" but it's the rule that is consistently the same
Phonetically the examples above are unambiguous though
Soft c = voiceless postalover affricate
https://en.m.wikipedia.org/wiki/Voiceless_postalveolar_affri...
hard c = Voiceless velar plosive
https://en.m.wikipedia.org/wiki/Voiceless_velar_plosive
They are not exactly what you write, but they have precise phonetic symbols expressing how they sound (which is not always how they look on paper)