If you need to cash in Italy, the bank will/could require you to cash in smaller instances (like 1000 € / day).
It is not against the law (for now) to cash or have large quantities of cash, but it is against the law to have any transaction of 1.000 € or more without using a traceable method (check, CC/DC, SEPA, etc.).
The law contemplate fines and jail time (in the worst case scenarios).
Obviously, people keep this law and the politicians in contempt.