I remember when first contactless payment options appeared, many people started buying anti-RFID wallets and bags. I'm not sure if they're still a thing, but the people who need "radio-privacy" will definitely find a way.
You'd also be surprised how powerful smart cards are these days. the aforementioned NXP chip has 586 KB ROM, 144 KB EEPROM and 11 KB RAM, crypto coprocessors for RSA/ECC/DES/AES, and a 32-bit CPU.