No. Link says it was a vulnerability in their website, so adding biometrics would've probably just meant your biometrics would've been leaked alongside your SSN.

Most are falsifiable and they are hard to do over the Internet (and are easier to fake over the internet). Also you can't change the info if there is a breach

Biometrics are more useful as an enhancing measure to verify identity but not for gaining access. Once compromised, it's forever.

One can even fake DNA if you have enough time, money and expertise...

Only until someone lifts your fingerprints or the like. And those are also difficult too change.

not if the digital ID with biometrics was on a public ledger and only you had the key....