e.g. Venice vs Venezia, Florence vs Firenze, etc. We don't do this for any other countries with Latin or Germanic-based languages, do we? So then why Italy?
The English actually do this with other countries with both Latin or Germanic-based languages as well (and Germans or French do this as well). Examples: Munich (München), Cologne (Köln), Brussles (Brüssel), Seville (Sevilla). Just to name a few from Germany, Belgium or Spain. Germans on the other hand call Venice Venedig and Florence is called Florenz.
This happens in every language I know, actually.
Firenze (Italian), Florence (English/French), Florenz (German)
München (German), Munich (English), Múnich (Spanish)
I even know some (older) people who say "Neu York" (the German word for new)
The reason is probably just that people are not always able to pronounce words/names in other languages.