Please fact check your €2,000 claim. There is several EU countries without a cash payment limit. In other countries, like Italy, the cash limit is €1,000. In most countries the cash limit is still €10,000. 
https://www.europe-consommateurs.eu/en/shopping-internet/cash-payment-limitations.html
https://www.europarl.europa.eu/news/en/press-room/20240419IPR20586/new-eu-rules-to-combat-money-laundering-adopted