This has nothing to do with Americans.
Nonsense. Read about FATCA.
The assumption is cash doesn’t get charged extra. No rights are being taken away.
Bad assumption. Cash payers are now being charged more, for train and bus tickets for example. A €10 ticket has an extra fee of €12 for paying cash (12 on top of the 10), for example.
Charges associated with useing cash for payments is handled with separate legislation, which is different in different parts of the EU because they use different currencies. Typically dealt with under laws relating to legal tender.
You are apparently unfamiliar with the Rundfunk case in Germany. The EU has exclusive competency over the euro and meaning of legal tender. And no, it does not protect cash payers from surcharges.