Cryptography could still prevent the usage of copies of valid passports. I.e. where you have all valid names and numbers on the front, but cannot copy the passport's secret key and digital signature.
EU passports support a further level of mutual authentication in order to get the fingerprints, where the terminal is verified by the passport as well.
There is a further step called Active Authentication where the reader sends the passport random data and it signs this data with a public key that can be verified as authentic.