In a case where a noun is a modifier of the following word, Italians tend to prefer specificity , therefore falling for the “noun + of…” construct.
A chicken soup bowl is easy to understand, but for an Italian that’s a “piatto di brodo di pollo”, so an Italian native would tend to feel like “a bowl of chicken soup” is the better choice.
In this case there’s no real mistake (and for “bowl of” you might argue there’s almost no meaning difference) but most of the time you end up with convoluted sentences, especially if a genitive is lurking around —-
“Andy’s chicken soup bowl” vs “the bowl of chicken soup of Andy”. Understandable, more familiar to an Italian speaker, yet kind of wrong.
Just for reference, the default English constructions would be "bowl of chicken soup" and "Andy's bowl of chicken soup".
"Bowl of soup of chicken" is right out, but "chicken soup bowl" isn't much better. It's so anomalous that I might interpret it as meaning "a bowl for chicken soup" as opposed to "a bowl with chicken soup in it right now".
Wouldn't "piatto di brodo di pollo" translate to "a bowl of soup of chicken", as a more unnatural English sentence?
Greek is similar in that respect and I catch myself sometimes lapsing into such more micro-managed speaking, and I also noticed it in other Greeks (perhaps a few Italians also).