Different people would associate different things according to their belief system, if they hold one.
A devout catholic would think of his god, goodness, the cross and sacrifice among others.
Someone of a different faith may associate opulence palaces, heresy.
No one symbol would fit all
it basically means that any new Pope who becomes Pope represents new Pope.
The Pope.
The pomegranate.
Pope Gregory I
Sure!
The Cow and the Peacock
Bunny rabbit
A bow and arrow.
Alexander Pope
The Crozier normally symbols an Archbishop so why does the pope have one? Very good question and the answer is that he technicly he was and archbishop before he became a cardinal or a pope.
Every individual pope has their own, unique insignia on their person. It is common practice for a pope to have his family crest on his person. Typically, displayed symbols reflect his aspirations.
Fast cars and football are probably the symbols most closely associated with Italy.