The maximum limit for cash payments in Italy is 1000€, so 3k would still be a lot. Why would someone need to pay for 10k in cash? Where does that cash come from? 60% of the times, it's money laundering every time. edit: I suppose since I'm in EU and I'm only 30 I'm "used" to the 1k limit, while non-EU (or specifically USA) people might be grabbing their pitchforks.
If you have $10,000, then you have $10,000.
If you deposit $10,000 in a bank, then you have $0 and a promise from a bank that has $1,000 and a promise (from somebody else) for $9,000.