If Passports had one's DNA data, it wouldn't help much at border crossings, because the Border Officers would hardly have time to collect saliva and analyse it while the enormously long queue waited.

It would only be helpful in individual cases of very important identity verification.
I think fingerprint ID would be helpful. A machine already exists which swiftly analyses fingerprints (one merely places the index finger on the glass)
Amazingly, Cote d'Ivoire already has biometric passports. My husband has to go down to London every five years to have his Ivorian one renewed at his Embassy. They measure his facial features and his eyes are scanned. So it wouldn't matter which gender he chose for himself.